Step-by-step explanation:
#3
Let's rewrite the equation in vertex form.
h(x) = -4x^2 + 24x - 41
h(x) = -4(x^2 - 6x) - 41
h(x) = -4(x^2 - 6x + 9) - 41 + 36
h(x) = -4(x - 3)^2 - 5
The vertex form is
f(x) = a(x - h)^2 + h
where point (h, k) is the vertex.
We see that h = 2, and k = -5.
The vertex is (3, -5).
The axis of symmetry is x = h.
The axis of symmetry is x = 3.
#5
The remainder theorem states that the remainder of synthetic division of the polynomial by x - c is the same as the value of the function evaluated at c. Here, c = 5, so we do the synthetic division using 5.
5| 1 9 15 -15 20
----- 5 70 425 2050
---------------------------------
1 14 85 410 2070
The remainder is 2070. That means that
f(5) = 2070
If k is a zero of function f, then f(k) = 0. Here, f(5) is not zero, so 5 is not a zero of the function.
