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
Statements 1 and 4 are correct. Let me know if you need more of an explanation. :)
Answer:
x = 2, y= -1 Or (2, -1)
Step-by-step explanation:
Let’s solve the system using substitution. First we can set the equations equal to each other:
x-3= -2x +3
Now solve for x
3x-3= 3
3x = 6
x=2
Now that we have x, we can plug it back into one of the original equations to get y
y= x-3
y= 2-3
y = -1
Finally, the solution to the system of equations is (2, -1).
Answer:
6x^2 + 4x
Step-by-step explanation:
g(x) + f(x)
= -8x^2 - 3x + 5 + 2x^2 + 7x - 5
= -8x^2 + 2x^2 - 3x + 7x + 5 - 5
= - 6x^2 + 4x
