Plot the x-intercept(s), y-intercept, vertex, and axis of symmetry of this function:
h(x) = (x − 1)2 − 9.

Part 1) The vertex is the point (1,-9)

Part 2) The equation of the axis of symmetry is x=1

Part 3) The y-intercept is the point (0,-8)

Part 4) The x-intercepts are (-2,0) and (4,0)

Part 5) The graph in the attached figure

Step-by-step explanation:

we have

This is a vertical parabola open upward

The vertex represent a minimum

Part 1) Find the vertex

The quadratic equation is written in vertex form

where

(h,k) is the vertex of the parabola

so

The vertex is the point (1,-9)

Part 2) Find the axis of symmetry

The equation of the axis of symmetry of a vertical parabola is equal the the x-coordinate of the vertex

so

The equation of the axis of symmetry is

Part 3) Find the y-intercept

we know that

The y-intercept is the value of the function when the value of x is equal to zero

so

For x=0

therefore

The y-intercept is the point (0,-8)

Part 4) Find the x-intercepts

we know that

The x-intercepts are the values of x when the value of the function is equal to zero

so

For h(x)=0

solve for x

square root both sides

therefore

The x-intercepts are (-2,0) and (4,0)

Part 5) Plot the graph of the quadratic function

Plot the following points to graph the function

vertex (1,-9)

axis of symmetry x=1

y-intercept (0,-8)

x-intercepts (-2,0) and (4,0)

The graph in the attached figure

f(x) has value 150 at x= 0

and 0 at x= 3

so d(f(x))/dt = slope = -150/3 = -50