What is the equation of the parabola with vertex (-2,5) and an x-intercept of x = 3

Step-by-step explanation:

if parabola has a vertex not in x-axis, it should have 2 x intercept

x-vertex = - 2

first x intercept = 3

second x intercept should - 7

so the equation will like this

y = a (x-x1) (x-x2)

y = a (x-3) (x+7)

y = a (x² + 4x - 21)

5 = a ((-2) ² + 4 (-2) - 21)

5 = a (4 - 8 - 21)

5 = a (-25)

a = 5 / (-25)

a = - 1/5

then the equation is

y = (-1/5) (x² - 4x - 21)

or you can write as

y = - x²/5 + 4x/5 + 21/5

or as this one

5y = - x² + 4x + 21