f(x)=-x^2+2x+24
f(1)=25
Justin's f(1) is wrong. Just exactly what is the question, anyway?
To find the x-intercepts, we set f(x) equal to zero and solve for x:
0 = -x^2 + 2x + 24
To solve this quadratic equation, we can use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
In this equation, a = -1, b = 2, and c = 24.
x = (-(2) ± √((2)^2 - 4(-1)(24))) / (2(-1))
Simplifying this expression further:
x = (-2 ± √(4 + 96)) / (-2)
x = (-2 ± √100) / (-2)
x = (-2 ± 10) / (-2)
We have two solutions for x:
x₁ = (-2 + 10) / (-2) = 8 / (-2) = -4
x₂ = (-2 - 10) / (-2) = -12 / (-2) = 6
Therefore, the x-intercepts of the function f(x) = -x^2 + 2x + 24 are x = -4 and x = 6.