Answer:
Part 1) Option 3 could be the quadratic equation shown in the figure
Part 2) Option 4
Step-by-step explanation:
Part 1) we know that
The quadratic equation shown in the graph represent a vertical parabola open downward
The vertex represent a maximum
The coordinates of the vertex are positive
The y-intercept is positive
Has two real solutions (x-intercepts) one positive and one negative
In this problem, the options 2 and 4 represent a vertical parabola open upward (because the leading coefficient is positive)
so
Options 2 and 4 could not be the quadratic equation shown in the figure
<u><em>Verify option 1 and 3</em></u>
Option 1
Find the y-intercept
The y-intercept is the value of y when the value of x is equal to zero
so
For x=0
The y-intercept is negative
therefore
Option 1 could not be the quadratic equation shown in the figure
Option 3
<em>Verify the y-intercept</em>
Find the y-intercept
For x=0
The y-intercept is positive
<em>Verify the vertex</em>
Convert to vertex form
Factor -2
Complete the square
rewrite as perfect squares
The vertex is the point (3,29)
so
Both coordinates are positive
<em>Verify the x-intercepts</em>
Remember that the x-intercepts are the values of x when the vakue of y is equal to zero
For y=0
square root bot sides
Has two real solutions (x-intercepts) one positive and one negative
therefore
Option 3 could be the quadratic equation shown in the figure
Part 2) we know that
Using a graphing tool
Plot the points
The quadratic equation represent a vertical parabola open downward
The vertex is a maximum
so
The maximum value of y is equal to 11 (based in the table)
so
see the attached figure to better understand the problem