Basic Math question and answers for October 23, 2024
- Q f(x)=x-16x +60(Type an ordered pair, using integers or fractions.)(b) Find an equation for the axis of symmetry.x=8(Type an equation. Use integers or fractions for any numbers in the equation.)(c) Determine...
- Q Which of the following describes the parabola with the equation y = 4x - 12x + 9?The axis of symmetry is x = -1.5 and the vertex is (-1.5, 36).The...
- Q Find the axis of symmetry for the parabola whose equation is given. Use the axis of symmetry to find a second point on the parabola whose y-coordinate is the same...
- Q Find the equation for thefollowing parabola.Vertex (2, -1)Focus (2, 3)A. (x-2) = (y+1)B. (x-2) =16(y+1)C. (x-2) = 4(y+1)D. (x-2) 16(y+1)
- Q A parabola has a vertex at (0,0). The focus of the parabola is located on the positive y-axis. In which direction must the parabola open? updownleftright
- Q Which equation represents the circle described?The radius is 2 units.The center is the same as the center of a circle whose equation is 2+2-8x-6y + 24 = 0.(x+4)2 + (y...
- Q A parabola can be represented by the equation x = - 20y.What are the coordinates of the focus of the parabola?(-5,0)(5,0)(0,5)(0,-5)
- Q A parabola with a vertex at (0,0) has a directrix that crosses the negative part of the y-axis.Which could be the equation of the parabola?x^2 = -4yx = 4yy =...
- Q Find the dimensions of a rectangle with a perimeter of 192 feet that has the maximum area. The side lengths are feet. (Use a comma to separate answers as needed.)
- Q Consider the following quadratic function.f(x)= 3x +6x-1(a) Write the equation in the form f(x)= a (x-h)+ k. Then give the vertex of its graph.Writing in the form specified: f(x) =Vertex:(b)...
- Q A parabola can be drawn given a focus of (1, 2) and a directrix of x = -11. Whatcan be said about the parabola?The parabola has a vertex at
- Q If you vertically shift the quadratic parent function, F(x) = x2, up seven units,what is the equation of the new function?A. G(x) = x +7B. G(x)=x2-7C. G(x) = 7xD. G(x)...
- Q If you horizontally compress the quadratic parent function, F(x)=x2, by 7 units, what is the equation of the new function?A. G(x) = (x+7)B. G(x) = 7xC. G(x) = (7x)D. G(x)=x-7
- Q Given that a parabola has its vertex at (-2, 1). Which of the following can not be the function expression of the parabola?f(x) = -(x + 2)+1f(x)=(x-2)+1f(x)=(x + 2)+1f(x)=3(x+2)+1
- Q A parabola has a vertex at (-1, -2) and opens down. Which of the following equations could represent the equation of this parabola in vertex form?y=2(x+1)2-6y=-2(x+1)-6y= 1/3 (x+1)-6y=-6(x+1)-2
- Q 1. Select the best choice for the definition of a parabola. *A. The graph of a quadratic function that is a U-shaped curve.B. Is defined by an ordered pair and...
- Q A quadratic equation can be written in vertex form or in standard form. Sometimes one form is morebeneficial than the other. Identify which form would be more helpful if you...
- Q Drag a value, coordinates, equation, or word to the boxes to correctly complete the statements.Gayle identifies that the vertex of the parabola is!units away from the vertex. The directrix is(3,-1)The...
- Q The parabola y = x +4 has two tangents which pass through the point (0, -4). One is tangent to the parabola at (A, A+4) and the other at (-A,...
- Q Consider the parabola given by the equation: f(x) = - 4x - 14x - 3Find the following for this parabola:A) The vertex:B) The vertical intercept is the pointC) Find the...
- Q A parabola that passes through the point (3, 52) has vertex (-7, 12). Its line of symmetry is parallel to the y-axis.Find equation of the parabola: y =When x =...
- Q Fill in the blanks Enter intercepts as ordered pairs, aka points. Then Graph the parabola given in vertex form.Vertex Form: y = (x + 4) - 11. Does the parabola...
- Q Graph the following quadratic function.f(x) = 7xFind the vertex of the function.The vertex is (0,0).(Simplify your answer. Type an ordered pair.)Find the y-intercept of the function.The y-intercept is (0,0).(Simplify your...
- Q Fill in the info below, and graph on your own paper. Then graph the parabola on the axes below by firstclicking on the vertex, and then on another point close...
- Q Find the points of intersection of the graphs of the equations.x + y = 19-4x + y = 14(x, y)= (smaller x-value)(x, y) = (larger x-value)
- Q If a parabola opens upward and has x-intercepts at (3, 0) and (-9, 0), what is the equation?y=a(x+3)(x-9), a < 0y = a(x-3)(x - 9), a < 0y = a(x+3)(x-9),...
- Q John O'Sullivan has just completed his first year in business. His records show that he spent the following in advertising:Internet $620 Radio $610 Yellow Pages $750 Local flyers $420What percent...
- Q Which way does the polynomial x = -3y + 1open?UpDownRightLeft
- Q Graph the parabola (do not place any dots) then fill in the blanks about the vertex, any intercepts, the domain, and range. Enter intercepts as ordered pairs, aka points.y =...
- Q Sketch the graph of the quadratic function.f(x) = 5x + 4Indicate the coordinates of the vertex, the y-intercept and the x-intercepts (if any). (If an answer does not exist, enter...
- Q 4. What is the equation of a parabola that passes through the points (-5, -10),(-3, 2), and (2, -3)?Ay=-x - 2x + 5By=-x + 6x - 7?y=-18x-28x +359y = -x...
- Q Find the r and y intercepts if they exist: y = x-4x - 12.
- Q Write the equation of the parabola in intercept form.y = x + 7x + 12y=(x+4)(x+3)y=(x-4)(x-3)y=(x-6)(x-2)y=(x+6)(x+2)
- Q Consider the quadratic function: f(x)A) The line of symmetry:B) The vertex:=- 2x - 10x + 12. Find the following for this parabola.C) The vertical intercept is the pointD) Find the...
- Q Graph the function. Label the vertex, axis ofsymmetry, and x-intercepts.y = 2(x + 2)(x+4)
- Q A dolphin dives down into the ocean and resurfaces along a path that is modeled by x2 - 8x + 4y = 0, where the distances are in feet. How...
- Q Lyra is designing a model of a solar system with a planet and a comet. The planet has a circular orbit, centered at the origin with a diameter of 140....
- Q The quadratic function whose graph is a bar parabola that opens upward has a minimum value, and the quadratic function whose graph is a parabola that opens downward has a...
- Q Graph the quadratic function in standard form y = 2(x - 1) - 8 A. Find the x-intercept(s). B. Find the y-intercept. C. Find the coordinates of the vertex. D....
- Q You're at the aquarium, staring into a large exhibit, whenyou look to your left and slightly downward and you see ajellyfish. You notice that the jellyfish body looks like a...
- Q Find the equation of the parabola described below. Find the two points that definethe latus rectum, and graph the equation.Vertex at (3, 4); focus at (3, ?6)CHICKEThe equation of the...
- Q Find the equation of the parabola described. Find the two points that define thelatus rectum, and graph the equation.3Directrix the line y=; vertex at (0,0)2.....What is the equation of the...
- Q Consider the following quadratic function.f(x)=3x+30x+71(a) Write the equation in the form f(x)= a (x-h)+k. Then give the vertex of its graph.(b) Graph the function. To do this, plot five points...
- Q Graph the parabola. y=-3x-30x-68 Plot five points on the parabola: the vertex, two points to the left of the vertex, and two points to the right of the vertex. Then...
- Q Sketch the following parabolas, labeling the coordinates of the vertex and focus and equation of the directrix:a. y + 2 = -1/4 (x - 1)Coordinates of vertex:Coordinates of focus:Equation of...
- Q f (x)=1/2x + 7x +69/2Axis of Sym.: x = 10Min value = 7Axis of Sym.: y = 10Max value = -7Axis of Sym.: x = -10Max value=7Axis of Sym.: x...
- Q f(x) = 3x + 54x +236Axis of Sym.: x=-11Max value = -5Axis of Sym.: y = 9Max value = 7Axis of Sym.: y = -7Max value = -9Axis of Sym.:...
- Q Use the graph of the function to answer parts (a) through (1).P(x) = -3(x+2) +1(a) Give the coordinates of the vertex.The coordinates of the vertex are (Type an ordered pair.)(b)...
- Q latus rectum, and graph the equation.3==; vertex at (0,0)2Directrix the line y:3What is the equation of the parabola?XE.y=6(Use integers or fractions for any numbers in the equation.)Find the two points...
- Q Given a quadratic functiony = (x - 1) -2Complete the following tasks. (2 points each)1. Find the vertex of the parabola.2. Write the equation of the axis of symmetry.3. Find...
- Q For the following quadratic function, (a) write the function in the form P(x)= a(x-h)2 + k, (b) give the vertex of the parabola, and (c) graph the function.P(x) = -2x...
- Q A jumping spider's movement is modeled by a parabola. The sider makes a single jump from the origin and reaches a maximum height of 20 mm halfway across a horizontaldistance...
- Q The inside of a flashlight surrounding the bulb is shaped like a parabola in which the base of the bulb represents the vertex and the top of the bulb represents...
- Q Graph the parabola.y = (x+3) +2Plot five points on the parabola: the vertex, two points to the left of the vertex, and two points to the right of the vertex.
- Q From the function f(x) = 2(x - 3) + 7choose ALL the statements below that are TRUEvertex is (3, 7)The vertex is (-3,7)There is a maximum value at 7The axis...
- Q A software engineer is creating a new computer software program. She wants to make sure that the crash rate is extremely low so that users would give high satisfaction ratings....
- Q Select the function that represents a parabola with vertex at (2,1) and y-intercept (0,3).A) f(x) = 2(x - 2) + 1B) f(x) = 2(x + 2) + 1C) f(x) =...
- Q Suppose the graph of y = ax + 6x + c has x-intercepts at the points (-2, 0) and(4,0).(a) Find the coordinates of the vertex and the equation of the...
- Q Todd hit a golf ball 250 yards. The maximum height the golf ball reached was 35 yards. Assume the path of the ball is parabolic. Write an equation for the...
- Q Find the equation of the quadratic function whose graph is a parabola containing the points (0,1), (3,25), and (-2,15).The equation of the quadratic function whose graph is a parabola containing...
- Q What is the vertex of the parabola y = -x + 7?(1,7)(5,6)(0,7)(7,0)(7,1)
- Q Consider the following quadratic function.f(x)=2x + 4x+5(a) Write the equation in the form f(x)= a (x-h) + k. Then give the vertex of its graph.(b) Graph the function. To do...
- Q OWhat is the directrix of the shape defined by theequation (y - 3)2 = -12x?x = -3y = 0Ox=1O y = 6x=3
- Q y - 3 = x + 12x +36Factor the perfect square trinomial, and solve for y.
- Q Which shape is defined by the equation y = 2x3?-O CircleO EllipseParabolaHyperbolaNone of the above.
- Q Write an equation for a parabola with x-intercepts (-3,0) and (4,0) which passes through the point (3,- 18).Write the equation.*****
- Q A parabolic mirror to be used in a searchlight measures 40 centimeters tall and 80 centimeters wide. It's light bulb needs to be placed at the focus for the light...
- Q A searchlight is shaped like a paraboloid of revolution. If the light source is located 1 feet from the base along the axis of symmetry and the opening is 6...
- Q A parabolic flashlight reflector is to be 8 inches across and 2 inches deep. Where should the lightbulb be placed?The lightbulb should be placed at inches from the vertex.
- Q True and False. Determine if each statement is true (T) or false (F), if false correct the statement to make it true.a. All quadratics have a degree of 2.b. When...
- Q Complete the square to find the vertex of the parabola y = 2x + 4x. Enter your answer as a point (h, k) including parentheses.
- Q Write the function whose graph is the graph of y = (x+4), but is reflected about the x-axis.
- Q Find the y-intercept and vertex for the following function: f(x) = 6x - 6x + c Express your answers in terms of c where appropriate.
- Q Consider the solid S described below.The base of S is the region enclosed by the parabola y = 4 - x and the x-axis. Cross-sections perpendicular to the x-axis are...
- Q In mountainous areas, reception of radio and television is sometimes poor. Consider an idealized case where a hill is represented by the graph of the parabola y = x -...
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