Question

Which function has a vertex at the origin?

f(x) = (x + 4)2
f(x) = x(x – 4)
f(x) = (x – 4)(x + 4)
f(x) = –x2

Answer 1

For any parent function \(\large\color{black}{ \displaystyle y=f(x) }\) (assuming it goes through the origin):

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\(\large\color{black}{ \displaystyle y=f(x+c) }\) is a shift \(c\) units to the left.
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\(\large\color{black}{ \displaystyle y=f(x-c) }\) is a shift \(c\) units to the right.
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\(\large\color{black}{ \displaystyle y=f(x)+c }\) is a shift \(c\) units up.
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\(\large\color{black}{ \displaystyle y=f(x)-c }\) is a shift \(c\) units down.
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\(\large\color{black}{ \displaystyle y=c{\tiny}f(x) }\) is stretching (widening) the function
when \(0<c<1\)
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\(\large\color{black}{ \displaystyle y=c{\tiny}f(x) }\) is making the function thiner and taller
when \(c>1\)

(this all is for positive number c)

Answer 2

\(\large\color{black}{ \displaystyle y=c{\tiny}f(x) }\) is called multiplying the function times the scale factor, and if the parent function y=f(x) is already going through the origin, then so would be the y=c•f(x) (regardless of value of c)

Answer 3

One note to make:

When c is a scale factor it can't equal zero, because the entire function then is going to be just a line y=0

Answer 4

if you got question(s), then please ask.... :)

Answer 5

no questions , btw
thanks