Answer:
f(x) = 4x^2 +7x -2
graph is attached
Step-by-step explanation:
The zeros of the function are at the ends of the open interval, so are -2 and 1/4. These are values that make the factors of f be zero. This means you can write the function as ...
f(x) = a(x +2)(4x -1) . . . . for some constant "a"
Then f(-1) = a(-1+2)(4(-1)-1) = a(1)(-5) = -5a. We know f(-1) = -5, so a=1 and the factored equation is ...
f(x) = (x +2)(4x -1)
Multiplying it out, we have ...
f(x) = 4x^2 +7x -2
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The axis of symmetry is halfway between the zeros, so is x = -7/8. This is where the minimum will be.
