Question

Determine the quadratic function whose graph is given
below.

Answer 1

The equation of the parabola in the image is:

y = (x + 3)² - 15

How to find the quadratic equation?

A quadratic equation with a vertex (h, k) and a leading coefficient A can be written as:

y = A*(x - h)² + k

Here we can see that the vertex is (-3, -15), then we can write the equation as:

y = A*(x + 3)² - 15

We also can see that the line passes through (0, -6), replacing these values we get:

-6 = A*(0 + 3)² - 15

-6 = 9A - 15

-6 + 15 = 9A

9 = 9A

9/9 = A

1 = A

then the equation is:

y = (x + 3)² - 15