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

y = 3x^2 - 42x + 144

Step-by-step explanation:

Looking at the information given, the minimum at (7,-3) is also the vertex of the parabola that would be formed if the graph is drawn. This minimum point is represented as (h,k). We will apply the vertex form of forming quadratic equations,

y = a(x - h)^2+ k

h = 7

k = - 3

Substituting Into the equation, it becomes

y = a(x - 7)^2 - 3

To find a, we will use the given point,

(9,9)

We will substitute x =9 and y = 9 into the equation, y = a(x - 7)^2 - 3. It becomes

9 = a(9 - 7)^2 - 3

9 = a × 2^2 - 3

9 = a×4 - 3

4a = 9 + 3 = 12

a= 12/4 = 3

The equation becomes

y = 3(x - 7)^2 - 3

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

y = 3(x^2 - 7x - 7x + 49) - 3

y = 3(x^2 - 14x + 49) - 3

y = 3x^2 - 42x + 147 - 3

y = 3x^2 - 42x + 144

the answer is 375 miles

step-by-step explanation: