Question

What is the value of g and r in the quadratic function f(x)=p(x−q)(x−r)f(x)=p(x−q)(x−r) if the graph passes through the points (-2, 0), (0, -4), and (4, 0)?

a) g=−2, r=4g=−2,r=4
b) g=0, r=−2g=0,r=−2
c) g=4, r=0g=4,r=0
d) g=−4, r=2g=−4,r=2

Write down the equation of the axis of symmetry.

a) x=−2x=−2
b) x=0x=0
c) x=2x=2
d) x=4x=4

Find the value of p.

a) p=−1p=−1
b) p=1p=1
c) p=−2p=−2
d) p=2p=2

Answer 1

The values of q and r in the quadratic function are -2 and 4 respectively, but the axis of symmetry and the value of p obtained from calculation, x=1 and p=-0.5, are not listed in the provided options, indicating a possible typo in the question.

Step-by-step explanation:

The given quadratic function is f(x) = p(x - q)(x - r). Since the graph passes through the points (-2, 0), (0, -4), and (4, 0), we can determine the values of q and r directly from the x-coordinates of the points where the function has a value of 0. These are the x-intercepts of the graph, so q = -2 and r = 4, which corresponds to option a) q = -2, r = 4.

The axis of symmetry of a quadratic function is exactly between the x-intercepts, which is the vertical line passing through the midpoint of -2 and 4. Therefore, the equation of the axis of symmetry is x = (q + r) / 2 = ( -2 + 4 ) / 2 = 1, which is not one of the provided options.

To find the value of p, we use another point the graph passes through, for instance, (0, -4). Substituting x = 0 into the function we get f(0) = p(0 - (-2))(0 - 4) = 8p, and since f(0) = -4, we solve for p: -4 = 8p, so p = -4 / 8 = -0.5. However, this value of p is also not given in the options, which suggests there may be a typo in the question or the provided options.