Question

Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar.

Determine the equation for the parabola graphed below.



y =
x2 +
x +

Answer 1

y = -2(x + 1)² + 7

y = -2x² - 4x + 5

Explanation:

Vertex: (-1,7)

y = a(x - -1)² + 7

y = a(x + 1)² + 7

Find a using (1,-1)

-1 = a(1 + 1)² + 7

-8 = 4a

a = -2

y = -2(x + 1)² + 7

y = -2(x² + 2x + 1) + 7

y = -2x² - 4x - 2 + 7

y = -2x² - 4x + 5

Answer 2

y = -2x^2 -4x +5

Explanation:

The vertex is at (-1,7) and the y intercept is at (0,5)

The vertex form of a parabola is

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

where (h,k) is the vertex

y = a(x--1)^2 +7

Then substitute the point into the equation

y = a(x+1)^2 +7

5 = a(0+1)^2 +7 +7

Subtract 7 from each side

5-7 = a(1)^2

-2 = a

y = -2(x+1)^2 +7

Now FOIL

y = -2 (x^2 +2x+1) +7

Then distribute

y = -2x^2 -4x-2 +7

y = -2x^2 -4x +5