F(x)=2x^2-x-10 part a: what are the x intercepts of the graph of f(x)? show your work
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
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

A. x intercepts are where the graph hits the x axis or where f(x)=0
0=2x^2-x-10
solve
hmm
we can use the ac method
multiply 2 and -10 to get -20
what 2 numbers muliply to get -20 and add to get -1 (the coefint of the x term)
-5 and 4
split the midd into that
0=2x^2+4x-5x-10
group
0=(2x^2+4x)+(-5x-10)
factor
0=2x(x+2)-5(x+2)
undistribute
0=(x+2)(2x-5)
set each to 0
0=x+2
0=-2

0=2x-5
5=2x
5/2=x

x intercepts are at x=-2 and 5/2 or the points (-2,0) and (5/2,0)

B. ok, so for f(x)=ax^2+bx+c
if a>0, then the parabola opens up and the vertex is a minimum
if a<0 then the parabola opens down and the vertex is a max

f(x)=2x^2-x-10
2>0
opoens up
vertex is minimum

ok, the vertex

the x value of  the vertex in f(x)=ax^2+bx+c= is -b/(2a)
the y value of the vertex is f(-b/(2a)) so
given
f(x)=2x^2-x-10
a=2
b=-1
-b/2a=-(-1)/(2*2)=1/4
f(1/4)=2(1/4)^2-(1/4)-10
f(1/4)=2(1/16)-1/4-10
f(1/4)=1/8-1/4-10
f(1/4)=1/8-2/8-80/8
f(1/4)=-81/8
so the vertex is (1/4,-81/8) or (0.25,-10.125)

C. graph the x intercepts and the vertex
the vertex is min and the graph goes through the x intercepts

12

Step-by-step explanation:

Use the Shoelace Theorem.

Area = ( 1/2 ) * { ( -4 * 8 ) + ( -8 * 2 ) + ( -8 * 8 ) - ( -8 * 8 ) - ( -8 * 8 ) - ( -4 *2 ) }

        = ( 1/2 ) * 24

        = 12

-> https://en.wikipedia.org/wiki/Shoelace_formula#Proof_for_a_triangle <-

[If there's any mistake, please inform me]