Question

Plot the x-intercept(s), y-intercept, vertex, and axis of symmetry of this function:

Answer 1

Answer:

Photo

Step-by-step explanation:

Answer 2

Answer:

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

$h(x)=(x-1)^2-9$

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

$y=a(x-h)^2+k$

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

$x=1$

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

$h(x)=(0-1)^2-9$

$h(0)=-8$

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

$(x-1)^2-9=0$

solve for x

$(x-1)^2=9$

square root both sides

$x-1=\pm3$

$x=1\pm3$

$x=1+3=4\\x=1-3=-2$

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