Respuesta :
Answer:
f(x) = 3(x-7)2+ -3 is equation
Step-by-step explanation:
Got it right on plato
The quadratic function has a minimum at (7,-3) and goes through is (9,9) [tex]y = 3(x - 7)^2 - 3[/tex].
Quadratic function
A quadratic function is one of the forms [tex]f(x) = ax^{2} + bx + c[/tex], where a, b, and c are numbered with a not equal to zero.
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,
[tex]y = a(x - h)^{2} + k[/tex]
h = 7
k = - 3
Substituting Into the equation, it becomes
[tex]y = a(x - 7)^2 - 3[/tex]
To find a, we will use the given point,
(9,9)
We will substitute x =9 and y = 9 into the equation,[tex]y = a(x - 7)^2 - 3[/tex]
It becomes
[tex]9 = a(9 - 7)^2 - 3[/tex]
[tex]9 = a * 2^2 - 3[/tex]
[tex]9 = a*4 - 3[/tex]
[tex]4a = 9 + 3 = 12[/tex]
a= 12/4 = 3
The equation becomes,
[tex]y = 3(x - 7)^2 - 3[/tex]
[tex]y = 3(x - 7)(x - 7) - 3[/tex]
[tex]y = 3(x^2 - 7x - 7x + 49) - 3[/tex]
[tex]y = 3(x^2 - 14x + 49) - 3[/tex]
[tex]y = 3x^2 - 42x + 147 - 3[/tex]
[tex]y = 3x^2 - 42x + 144[/tex]
To learn more about Quadratic function refer to:
https://brainly.com/question/2236333
#SPJ2
