Question

Given the function f(x) = -x^2+8x
a. Determine the vertex,
b. List the axis of symmetry,
c. calculate the y-intercept,
d. find an additional point on the graph, and
e. graph the function.
Please show all of your work. Given the function f(x) = -x^2+8x
a. Determine the vertex,
b. List the axis of symmetry,
c. calculate the y-intercept,
d. find an additional point on the graph, and
e. graph the function.
Please show all of your work. @Mathematics

Answer 1

\[vertex = (\frac{-b}{2a}, f(\frac{-b}{2a}))\] So it would be \[\frac{-8}{-2}\] which is 4.. So now plug in 4 into the equation \[f(4) = -(4)^2 + 8(4)\] Which is 16.. So the vertex is at \[(4, 16)\]

Answer 2

Axis of symmetry is the x value of the vertex.. So Axis of Symmetry is \[x = 4\]

Answer 3

The y- intercept is found by plugging x to be 0. So you do \[f(0) = -(0)^2 +8(0)\] So the\[y-intercept = (0,0)\]

Answer 4

For part d. pick any value of x and find its corresponding y value.. Im choosing 1 \[f(1) = -(1)^2 + 8(1)\] That is 7.. So another point on the graph is (1,7)