The vertex of a parabola is (-1.5, -12.5), and its y-intercept is (0, -8). The x-intercepts of the parabola are __(1)__ and __(2)___.<

Question

The vertex of a parabola is (-1.5, -12.5), and its y-intercept is (0, -8).
The x-intercepts of the parabola are __(1)__ and __(2)___.

1: Answer Choices
(-2,0)
(-4,0)
(2,0)
(4,0)

2: Answer Choices
(-1,0)
(2,0)
(1,0)
(-2,0)

0

Answers ( No )

    0
    2022-01-11T18:38:27+00:00

    The vertex form of the equation of the parabola is:

    y = A(x – h)^2 + k

    Where h and k are the x and y – coordinates of the vertex.

    In this case h = – 1.5 and k = – 12.5, so you know that the equation of this parabola is:

    y = A(x + 1.5)2 – 12.5

    The y-intercept is the y-value when x = 0, so you know:

    – 8 = A(0 + 1.5)^2 – 12.5, from which you can solve for A:

    – 8 = A (1.5)^2 – 12.5

    A(1.5)^2 = – 8 + 12.5

    A = 4.5 / (1.5)^2 = 2.

    And now you have the equation of the parabola: y = 2(x + 1.5)^2 – 12.5

    The x-intercepts are the x-values when y = 0

    => 2(x + 1.5)^2 – 12.5 = 0

    => (x + 1.5)^2 = 12.5 / 2

    (x + 1.5)^2 = 6.25

    => (x + 1.5) = +/- √6.25

    (x + 1.5) = +/- 2.5

    => x = -1.5 +/- 2.5

    => x = – 1.5 + 2.5 = 1 and x = -1.5 – 2.5 = – 4

    => (1,0) and (-4,0)

    Answer: (-4,0) and (1,0)

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