My assignment is late and i'm stuck on this question! ( explain fully but keep it simple)

an expression is shown below:

f(x) = 2x2 − 3x − 5

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 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)

A)

f(x) = 2x2 − 3x − 5

To find the x intercepts, set the equation to equal 0 and solve for x:

2x^2 - 3x -5 = 0

Factor by grouping:

2x^2 - 5x +2x -5 = 0

x(2x-5) +1(2x-5)=0

(2x-5)(x+1)=0

x= 5/2 and x = -1

X-intercepts = (5/2,0) and (-1,0)

B)

In the given equation a = 2, b = -3 and c = -5

Use those values to find the vertex:

Vertex form is a(x +d)^2 +e

D = b/a^2 = -3/2^2 = -3/4

E = c - b^2/4a = -5 - -3^2/4(2) = -49/8

Replace the letters with their values:

2(x-3/4)^2 - 49/8

The vertex is (3/4, -49/8)

Because the Y value is negative, the vertex is a minimum ( below 0)

C) You would then need to find the Y - intercept by replacing x with 0 in the original equation to get ( 0,-5)

Now you have 4 sets of coordinates to plot on a graph, then connect with a line forming a parabola.