Use the function f(x) = 5x2 + 2x − 3 to answer the questions.
part a: completely factor f(x). (2 points)
part b: what are the x-intercepts of the graph of f(x)? show your work. (2 points)
part c: describe the end behavior of the graph of f(x). explain. (2 points)
part d: what are the steps you would use to graph f(x)? justify that you can use the answers obtained in part b and part c to draw the graph. (4 points)

see below.

step-by-step explanation:

part a.

5x^2 + 2x - 3

= 5x^2 + 5x - 3x - 3

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

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

part b.

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

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

x = 3/5,   -1.

the x-intercepts are (3/5, 0) and (-1, 0).

part c.

the equation is a quadratic and the leading coefficient (5) is positive so its a parabola which opens upwards. the end behaviour is a curve rising to the right.

part d.

to graph the equation you would mark the x -intercepts   at (3/5, 0 ) and (-1,0). the y intercept is when x = 0 so it is y = 5(0)^2 + 2(2) - 3 = (0, -3) so you would mark this point.

now you know it opens upwards from part c so the next step is to find the   minimum value of f(x) - that is the vertex.

convert to vertex form:

5x^2 + 2x - 3

= 5( x^2 + 0.4x) - 3

= 5 ( (x + 0.2)^2 - 0.04) - 3

= 5(x + 0.2)^2 -3.2 so the vertex is at (-0.2, -3.2) . mark this point.

finally draw the curve through the 4 points you have marked.