Vertical Shifts of Quadratic Functions

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

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Key Questions

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

    Given a simple quadratic function:


    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:


    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.

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

    So, the y-intercept of #f(x)=ax^2+bx+c# is


    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.