IDNLearn.com provides a user-friendly platform for finding and sharing accurate answers. Our experts provide timely and precise responses to help you understand and solve any issue you face.
The quadratic equation with the given characteristics is:
f(x) = (x + 3)*(x - 7).
We know that the vertex must be (2, -25) and it passes through (7, 0).
For a quadratic equation:
y = a*x^2 + b*x +c
The x-value of the vertex is:
x = -b/2a
Then we have:
2 = -b/2a
We also have:
-25 = a*4 + b*2 + c
And because the function passes through (7, 0) we know that 7 is one of the roots, then:
0 = a*49 + b*7 + c
Then we have 3 equations to work with:
2 = -b/2a
-25 = a*4 + b*2 + c
0 = a*49 + b*7 + c
If we subtract the third and second equations we get:
25 = a*45 + b*5
Now, with the first equation we can rewrite:
a = -b/4
Replacing that in the other equation:
25 = a*45 + b*5
25 = (-b/4)*45 + b*5 = b*(-25/4)
25*(-4/25) =b = -4
Now we know the value of b.
2 = -(-4)/2a
a = 1
Now we need to find the value of c, we have that:
0 = 1*49 + -4*7 + c
0 = 49 - 28 + c
0 = 21 + c
Then c = -21
The equation is:
[tex]y = x^2 - 4x - 21[/tex]
It can be factorized to:
f(x) = (x + 3)*(x - 7).
If you want to learn more about quadratic equations:
https://brainly.com/question/1214333
#SPJ4