Answer:
Part A : All real numbers less than or equal to 4.
Part B : f(x) = x² + 3x - 40
Part C : a + b = 1
Part D : (4,0) and [tex](-\frac{5}{2}, 0)[/tex]
Part E : 5
Step-by-step explanation:
Part A :
From the given graph the y-value lies between 4 ≥ y ≥ - ∞.
Therefore, the range of the function f(x) = - (x + 5)(x + 1) will be all real numbers less than or equal to 4. (Answer)
Part B :
We have to find the function which has real zeros at x = - 8 and x = 5.
Now, (x + 8) and (x - 5) will be the factors of the quadratic function and hence, f(x) = (x + 8)(x - 5)
⇒ f(x) = x² + 3x - 40 (Answer)
Part C :
If ax² + bx + c = 0 is a quadratic equation having roots α and β then sum of the roots i.e. α + β = - b/a.
Here, the equation x² - x - 90 = 0 has roots a and b, then [tex]a + b = - \frac{- 1}{1} = 1[/tex] (Answer)
Part : D
The x-intercept of the function f(x) = - 2x²- 3x + 20 will be at f(x) = 0.
So, - 2x² + 3x + 20 = 0
⇒ - 2x² + 8x - 5x + 20 = 0
⇒ (x - 4)(- 2x - 5) = 0
So, either x = 4 or [tex]x = - \frac{5}{2}[/tex]
Therefore, the x-intercept will be at (4,0) and [tex](-\frac{5}{2}, 0)[/tex]. (Answer)
Part : E
(0, -3) and (2,7) are the two ordered pair of the function f(x) = 2x² + x - 3.
Therefore, the rate of change for the interval between x = 0 and x = 2 of the function will be
[tex]\frac{7 + 3}{2 - 0} = 5[/tex] (Answer)
