Question

Factor the expression completely:
4x^2 - 8x - 140
&
x^2 - 64

Show work

Answer 1

@e.mccormick @austinL @AkashdeepDeb @genius12 @myininaya Please help, I need this ASAP

Answer 2

Given the function: f(x) = 4(x - 5)^2 + 6 First, identify the vertex:

Then tell how each shift will affect the graph:
f(x + 1)
f(x) + 2
f(-3x)

Answer 3

@tHe_FiZiCx99 @thomaster Please help

Answer 4

First question

4x^2 - 8x - 140

4(x2 - 2x - 35)
4(x2 - 7x + 5x - 35) [SPLIT THE MIDDLE TERM]

4{x(x-7) + 5(x-7)}
4(x+5)(x-7)

ULTIMATE FACTOR FORM! \m/

Answer 5

For the second question use this theorem.
\[a^2 - b^2 = (a+b)(a-b)\]
The 2 terms are perfect squares so it should be easy. :)

Answer 6

Third question

f(x) = 4(x - 5)^2 + 6

Simplify the equation to get the individual a,b,c standard values.

This is a parabola and thus to find the vertex you may use the vertex co-ordinate formula

=> V(x,y) = V(\(\frac{-b}{2a} , c - \frac{b^2}{4a}\))

Answer 7

Fourth question

Anything done to the x value will shift it in the opposite direction by the same number of units added/subtracted along the x-axis.

Thus f(x+1) should move f(x) 1 unit to the left.

Answer 8

Fifth question

Anything added/subtracted to f(x) would move the entire graph, the same number units up or down along the y-axis.

Thus f(x) +2 will move it 2 units upwards along the y-axis.

Answer 9

Sixth question

When anything is multiplied to the x value it makes it narrower, if it is divided by any magnitude it'll become more wider.

When f(x) becomes f(-x) it mirrors itself along the y-axis.
ie. -x^3 is the mirror image of x^3 and same with all other functions!

So f(-3x) would be narrower and the mirror image of the original graph f(x)

Answer 10

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Understood all of this? :)