Question

(Essay Worth 10 points)
(08.01 HC)
Use the function f(x) to answer the questions:
f(x) = 5x²+2x-3
Part A: What are the x-intercepts of the graph of f(x)? Show your work. (2 points)
Part B: Is the vertex of the graph of f(x) going to be a maximum or a minimum? What are the coordinates of the vertex? Justify your answers and show your work. (3 points)
Part C: What are the steps you would use to graph f(x)? Justify that you can use the answers obtained in Part A and Part B to draw the graph. (5 points)

1. diemthu
The vertex of the function is a minimum and the coordinate of the vertex of the function is (0.2, -2.4)

### Part A: What are the x-intercepts of the graph of f(x)

The function is given as:
f(x) = 5x^2 + 2x – 3
Expand the function
f(x) = 5x^2 + 5x – 3x – 3
Factorize the function
f(x) = (5x – 3)(x + 1)
Set the function to 0
(5x – 3)(x + 1) = 0
Solve for x
x = 3/5 and x =-1
Hence, the x-intercept is 3/5 and -1

### Is the vertex of the graph of f(x) going to be a maximum or a minimum?

The vertex of the function is a minimum.
This is so because the leading coefficient of the function is positive

### What are the coordinates of the vertex?

Here, we have:
f(x) = 5x^2 + 2x – 3
Differentiate and set to 0
10x + 2 = 0
Solve for x
x = -0.2
Substitute x = -0.2 in f(x) = 5x^2 + 2x – 3
f(0.2) = 5(0.2)^2 + 2(0.2) – 3
Evaluate
f(0.2) = -2.4
Hence, the vertex of the function is (0.2, -2.4)

### What are the steps you would use to graph f(x)?

To do this, we simply plot the x-intercept and the vertex.
And then connect the points