What is the equation of the quadratic function that has a minimum at (7,-3) and goes through (9,9) ?

y = 3x² - 42x + 144

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) = (7, - 3), thus

y = a (x - 7) ² - 3

To find a substitute (9, 9) into the equation

9 = 4a - 3 (add 3 to both sides)

12 = 4a (divide both sides by 4)

a = 3

y = 3 (x - 7) ² - 3 ← in vertex form

Expand factor and simplify

y = 3 (x² - 14x + 49) - 3

= 3x² - 42x + 147 - 3

= 3x² - 42x + 144 ← in standard form