The quadratic equation is y = -2x² - 16x - 29
How to find the quadratic equation?
A quadraitc equation with a leading coefficient a and a vertex (h, k) can be written as:
y = a*(x - h)² + k
Here the vertex is at (-4, 3), then we will get:
y = a*(x + 4)² + 3
The curve also passes through (-3, 1), then:
1 = a*(-3 + 4)² + 3
1 = a*1 + 3
1 - 3 = a1
-2 = a
Then the quadratic is:
y = -2*(x + 4)² + 3
Expánding the product:
y = -2(x² + 8x + 16) + 3
y = -2x² - 16x - 32 + 3
y = -2x² - 16x - 29