Question

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)

Answer 1

Answer:

Solution:

Part A:

put f(x)=0

5x²+2x-3=0

5x²+5x-3x-3=0

5x(x+1)-3(x+1)=0

(x+1)(5x-3)=0

x+1=0, 5x-3=0

x=-1, x=3/5

Part B:

f(x)=5x²+2x-3

=5[x²+(2/5)x]-3

=5[x²+(2/5)x+(4/100)-(4/100)]-3

=5[(x+(2/10)]²-(4/20)-3

=5[(x+(2/10)]²-64/20

since f(x)=a(x-h)²+k; (h, k) is the vertex of f(x)

so vertex of the graph of f(x) is going to be a minimum because a=5>0 and so the vertex (h, k)=(-2/10, -64/20)=(-1/5, -16/5).

Part C:

I would use to graph of f(x) by the following steps:

1. to draw the x-intercept of the graph of f(x).

2. to draw the vertex of the graph of f(x).

3. to check the condition that whether a>0 or a<0 to draw minimum or maximum, respectively of the graph of f(x).