When you know the vertex and at least one other point:

Use the equation for vertex form, plugging in your vertex for h and k.

Now you just need to find a.

Plug in the x and y values of your other point into your equation for x and y.

Solve for a.

Here's an example where the vertex is (55, 100) and another point on the parabola is (0, 10).

Rewrite the equation with x and y as variables again:

Use the Distributive Property and Properties of Equality to put the equation in standard form

When you know any three points:

You can use a spreadsheet and regression to find an equation for your parabola.

Enter the three points into the spreadsheet. Here's an example with points (0, 10), (2, 14), and (10, 10):

Highlight the data, then insert a chart, choosing the "XY (Scatter)" option.

Click on one of the points on the graph. Choose "Add Trendline..." from the Chart menu.

Choose Polynomial and make sure the Order is 2 (Order actually mean degree!).

Click on Options and click the checkbox next to "Display Equation on Chart."

Your equation will show up on the graph. For this example, the equation is y = -0.25x^2 + 2.5x + 10.

If you don't know the vertex, you will have to complete the square to find the vertex form for your equation.

Completing the Square

Here is a continuation of the above example. We subtract 10 from both sides, then divide everything by -0.25.

A Few Formulas

Standard form: y = ax^2 + bx + c, where a ≠ 0; the point (0, c) is the y-intercept.

Vertex form: y - k = a (x - h)^2, where the point (h, k) is the vertex.

Factored form: y = a (x - r1) (x - r2), where r1 and r2 are the x-intercepts. The points (r1, 0) and (r2, 0) are the x-intercepts.

Discriminant: The discriminant is b^2 - 4ac. It tells you how many solutions (x-intercepts) there are, as well as whether or not the equation can be factored over the integers.

Quadratic Formula:

Technology Help

If you are using Grapher, you can upload your graph to the wiki. After setting the appropriate Frame Limits and entering your equation, choose "Export..." from the File menu. Choose JPEG as the file format. Then upload it to your wiki page (see below).

If your graph is on Microsoft Excel, right-click on the white background part of the graph and choose "Save as Picture..." Choose JPG as the Format. Then upload it to your wiki page (see below).

To upload a picture to the wiki, click the "File" button on your Editor bar. Click "Upload File" then choose your image file. Wait for it to upload. When it shows up in the list, double click on it and it will be on your wiki page!

## Help!

This page contains information on various topics that may help on your Chapter 12 Project.## Table of Contents

## Writing Equations

When you know the vertex and at least one other point:handk.a.xandyvalues of your other point into your equation forxandy.a.xandyas variables again:When you know any three points:y= -0.25x^2 + 2.5x+ 10.## Completing the Square

## A Few Formulas

y=ax^2 +bx+c, wherea≠ 0; the point (0,c) is they-intercept.y-k=a(x-h)^2, where the point (h,k) is the vertex.y=a(x- r1) (x- r2), where r1 and r2 are thex-intercepts. The points (r1, 0) and (r2, 0) are thex-intercepts.b^2 - 4ac. It tells you how many solutions (x-intercepts) there are, as well as whether or not the equation can be factored over the integers.## Technology Help