Question

How are the graphs y = kx^2 y = k(x-a)^2 related

Answer 1

I don't want the answer but a hint

Answer 2

often, graphing will help show you

https://www.desmos.com/calculator/m4tjarhbc4

Answer 3

btw you can replace k and a with any numbers you want

in my case, I used k = 1 and a = 2

Answer 4

nice figure, yeah so it seems that the graph is shifted to the right by a units.

Answer 5

correct

Answer 6

if 'a' is negative, then the graph shifts to the left |a| units

Answer 7

you can move the sliders to see it in action

Answer 8

@jim_thompson5910 yeah I'm starting to see this. when a is -ve the graph moved to the left by a units.

Answer 9

is there a specific name for the form k(x-a)^2?

Answer 10

for the function \(f(x)\) we have that \(f(x+a)\) movies the graph \(a\) units to the left.

Answer 11

it's vertex form

http://mathbitsnotebook.com/Algebra1/Quadratics/QDVertexForm.html

though they used k in a different spot

Answer 12

question is vertex the same as axis of symmetry or no?

Answer 13

\[y = k(x-h)^{2}+k \]

Answer 14

the vertex is a point (in this case, the point (a,0))
the axis of symmetry is a vertical line (in this case, y = a)