Quadratic Relations

What is the point $\left(h,k\right)$(`h`,`k`) on the parabola defined by the equation $y=a\left(x-h\right)^2+k$`y`=`a`(`x`−`h`)2+`k`?

$y$`y`-intercept

A

Vertex

B

Axis of symmetry

C

$x$`x`-intercept

D

Easy

Less than a minute

Consider the equation $y=\left(x+1\right)^2$`y`=(`x`+1)2.

Consider the quadratic function $f\left(x\right)=\left(x-3\right)^2$`f`(`x`)=(`x`−3)2.

Consider the quadratic function $h\left(x\right)=\left(x+5\right)^2$`h`(`x`)=(`x`+5)2.

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Sketch, by hand, the graph of y = a(x – h )^2 + k by applying transformations to the graph of y = x^2