Question

**** WILL FAN AND MEDAL ****
Determine whether each quadratic function intersects the x-axis at one point, two points or not at all.
a) g(x)= 4(x-6)^2+2
b) f(x)=-3(x-5)^2+2
c) f(x)= -3(x+2)^2

Answer 1

It going to take a while to the answer so please wait patiently :3

Answer 2

@TypnoEchosis Do you understand how to solve these questions?

Answer 3

Yes O 3O

Answer 4

well for part a) I'm not sure if i have to foil or not

Answer 5

Oh okay

Answer 6

So, do i have to use the foil method?

Answer 7

Yes use the foil method

Answer 8

Do both the foil and non-foil method and see what you get. It really helps :)

Answer 9

g(x)=4(x-6)^2+2
=4(x-6)(x-6)+2
=4(x^2-6x-6x+36)+2
=4(x^2-12x+36)+2

What do i do next?
do i distribute 4 into the brackets? Or factor? ( finding two numbers which multiply to 36 and add to -12)

Answer 10

@TypnoEchosis ^^

Answer 11

Yes distrubute 4 into brackets

Answer 12

Doing this is basically like doing order of operations except much more complicated.

Answer 13

=4(x^2-12x+36)+2
=4x^2-48x+144+2
=4x^2-48x+146

Answer 14

b^2-4ac=(-48)^2-4(4)(146)
=2,304-2,336
=-32

@TypnoEchosis The parabola will not intersect the x-axis?

Answer 15

is that right?

Answer 16

a) not at all
b) two point intersection
c) one point (tangent to the x axis at one point)

A two page solution with plots is attached.

Answer 17

The attachment was produced by Mathematica v9 .

Answer 18

thank you!