Answer:
f(x) = 2(x + 3)² - 7
Explanation:
f(x) = a(x - h)² + k - an equation for the parabola with vertex (h, k)
f(x) = a(x - (-3))² + (-7) - an equation for the parabola with vertex (-3, -7)
f(x) = a(x + 3)² - 7
The parabola going through point (-2,-5) so if x = -2 then f(x) = -5
- 5 = a(-2 + 3)² - 7
- 5 + 7 = a(1)² - 7 + 7
2 = 1a
a = 2
So an equation for the parabola with vertex (-3, -7) and point (-2,-5)
f(x) = 2(x + 3)² - 7