9.2 Graphing Quadratic Equations Algebra 1

Quadratic function Standard form Every quadratic function has a U-shaped graph called a parabola. Vertex is the lowest or highest pt of the parabola. Axis of symmetry – line passing thru the vertex, dividing the U in half.

Graph of a Quadratic function

Steps to graph a quadratic f(x) 1) Use to find half of the vertex and axis of symmetry. 2) Substitute the x value into the equation to find the y value of the vertex. 3) Use the vertex to make your T-chart to find 4 other points on the parabola.

Example 1 Solve by graphing. 1.) 2.) Substitute 3.) T-chart

Graph of Ex. 1

Ex. 2 #63 on pg. 522

Graph of Ex. 2

Assignment

Example 1, Step 3 x l y -2 l -1 l 0 l 1 l 2 l

Example 1 – Substitute each value into the equation. x l y -2 l -8 -1 l 0 l 1 l 2 l

Example 1- Substitute -1 x l y -2 l –8 -1 l –9 0 l 1 l 2 l

Example 1 – Substitute 0 x l y -2 l –8 -1 l –9 0 l –8 1 l 2 l

Example 1 – Substitute 1 x l y -2 l –8 -1 l –9 0 l –8 1 l –5 2 l

Example 1 – Substitute 2 x l y -2 l –8 -1 l –9 0 l –8 1 l –5 2 l 0

Example 1 Did you see that we had a zero as the y value on our last point, (2,0)? This is one of the roots or zero’s. Once, you graph it you should see that the parabola also crosses the x-axis at –4. Which is the other answer we found when factoring. I hope that you can graph this example on graph paper to see what I am referring to. Good Luck!

A quadratic equation… is an equation in which the value of the related quadratic function is 0.

Example 1 Solve by Factoring (x+4)(x-2)=0 x+4=0 x-2=0 x=-4 x=2

Roots and Zero’s For example, . We have used factoring to solve for x or the “roots”. The x values are the x-intercepts or the “zero’s” of the equation. They are called the “zero’s” because the y value is zero in the ordered pair. Let’s find the zero’s of this example.