Question

Suppose a parabola has vertex (6, -3) and also passes through the point (8,5).

Write the equation of the parabola in vertex form.

(Answers are given in photo)

10 points!!! Please help.

Answer 1

Answer: D. y = 2(x - 6)^2 - 3

Step-by-step explanation: see attachment. i hope this helped :)

Answer 2

The equation of the parabola that has vertex (6, -3) and also passes through the point (8,5) is $y = 2(x - 6)^2-3$

The vertex form of the equation of a parabola is:

$y = a(x - h)^2 + k$

where the vertex = (h, k)

The given vertex, (h, k) = (6, -3)

The line passes through the (8, 5)

x  =  8,  y  =  5

Substitute x = 8, y = 5, h = 6, y = -3 into the equation to solve for a

$y = a(x - h)^2 + k$

$5 = a(8 - 6)^2 + (-3)\\5 = a(2^2)-3\\4a = 5 + 3\\4a = 8\\a = \frac{8}{4} \\a = 2$

Substitute a = 2, h = 6, k = -3 into $y = a(x - h)^2 + k$

$y = 2(x - 6)^2-3$

The equation of the parabola that has vertex (6, -3) and also passes through the point (8,5) is $y = 2(x - 6)^2-3$

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