Answer:
Part A) The x-intercepts are the points (-2.5,0) and (0.5,0)
Part B) The vertex is a minimum and the coordinates are (-1,-9)
Part C) see the explanation
Step-by-step explanation:
we have
Part A: What are the x-intercepts of the graph of f(x)?
we know that
The x-intercepts are the values of x when the value of the function f(x) is equal to zero
so
For f(x)=0
Solve the quadratic equation
The formula to solve a quadratic equation of the form
is equal to
in this problem we have
so
substitute in the formula
therefore
The x-intercepts are the points (-2.5,0) and (0.5,0)
Part B: Is the vertex of the graph of f(x) going to be a maximum or minimum? What are the coordinates of the vertex?
we know that
The quadratic equation represent a vertical parabola open upward (because the leading coefficient is positive)
therefore
The vertex represent a minimum
Convert to vertex form
Factor 4
Complete the square
Rewrite as perfect squares
----> equation in vertex form
The vertex is the point (-1,-9)
Part C: What are the steps you would use to graph f(x)?
To graph f(x)
I need
1) The direction of the graph (Is a vertical parabola open upward)
2) The coordinates of the vertex (-1,-9) ( in this case is a minimum)
3) The x-intercepts (-2.5,0) and (0.5,0)
4) The y-intercept
The y-intercept is the value of f(x) when the value of x is equal to zero
so
For x=0
The y-intercept is the point (0,-5)
Plot the points and draw the parabola
see the attached figure to better understand the problem