# Vertical Shifts of Quadratic Functions

10.2 Example 1 Graphing Quadratics (Vertical Shift)
4:51 — by Tim McCaffrey

Tip: This isn't the place to ask a question because the teacher can't reply.

## Key Questions

• Vertical Shifts are just how much a function is shifted or moved up the y axis.

Given a simple quadratic function:

$y = {x}^{2} + 2$

graph{x^2+2 [-10, 10, -1, 9]}

You can see from the graph this function that the parabola is 2 units above the origin because it has a vertical shift of 2 after its parent function. In this case, the parent function is:

$y = {x}^{2}$

You will not always be able to easily find the vertical shift of a quadratic equation, but if the function is in vertex form, then the vertical shift can be found easily from its 'k'.

More on vertex form can be found here.
http://www.purplemath.com/modules/sqrvertx.htm

• In order to find the y-intercept $b$ of any function $f \left(x\right)$ is $f \left(0\right)$.

So, the y-intercept of $f \left(x\right) = a {x}^{2} + b x + c$ is

$f \left(0\right) = a {\left(0\right)}^{2} + b \left(0\right) + c = c$.

The constant term c of a quadratic function is always its y-intercept.

I hope that this was helpful.

• I would start with its vertex, then move either to the right or to the left, then use a symmetry to draw the other half.

I hope that this was helpful.

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