Question

Find the parabola through

(
−
7
,
−
39
)
(
-
7
,
-
39
)
with vertex
(
−
4
,
−
12
)

Answer 1

y = - 3x² - 24x - 60

Explanation:

The equation of a parabola in vertex form is

y = a(x - h)² + k

where (h, k) are the coordinates of the vertex and a is a multiplier

Here (h, k) = (- 4, - 12 ), thus

y = a(x + 4)² - 12

To calculate a substitute (- 7, - 39) into the equation

- 39 = a(- 7 + 4)² - 12 ( add 12 to both sides )

- 27 = 9a ( divide both sides by 9 )

- 3 = a

y = - 3(x + 4)² - 12 ← in vertex form

Expand (x + 4)²

y = - 3(x² + 8x + 16) - 12

= - 3x² - 24x - 48 - 12

y = - 3x² - 24x - 60 ← in standard form

= - 3(x²