Question

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

Answer 1

Answer:

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