Hat is the equation of the quadratic function with a vertex at (2,-25) and an x-intercept at (7,0) ?

y = x² - 4x - 21

Step-by-step 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) = (2, - 25), thus

y = a (x - 2) ² - 25

To find a substitute (7, 0) into the equation

0 = a (7 - 2) ² - 25 = a (5) ² - 25 = 25a - 25 (add 25 from both sides)

25a = 25 (divide both sides by 25

a = 1, thus

y = (x - 2) ² - 25 ← in vertex form

Expand and simplify

y = x² - 4x + 4 - 25

y = x² - 4x - 21 ← in standard form