Solving Quadratic Equations Graphically

Tutoring on Solving Quadratic Equations Graphically

Learning Objectives:

Understand to Solve Quadratic Equations Graphically

Math Tutoring on Solving Quadratic Equations Graphically

A quadratic is a polynomial that looks like ax² + bx + c, where a, b and c are just numbers. A quadratic equation as you remember is an equation that can be written on the standard form ax²+bx+c=0, where a≠0. You know by now how to solve a quadratic equation using factoring. Another way of solving a quadratic equation is to solve it graphically. The roots of a quadratic equation are the x-intercepts of the graph. The zeros of a quadratic equation are the points where the graph of the quadratic equation crosses the x-axis. Following are the steps to solve quadratic equations graphically: 

Step 1: Determine which form of quadratic equation we have, i.e.

 1) Standard form f(x) = ax² + bx + c where a, b, and c are real numbers and a is not equal to zero.

2) Vertex form f(x) = a(x - h)² + k where a, h, and k are real numbers and a does not equal zero. 

Step 2: Define your variables a, b, and c (or a, h, and k). 

Step 3: Calculate h and k. Plot the vertex.  

Step 4: If necessary, find and plot the x and y intercept.   

Step 5: If necessary, plot additional points, then graph.

 

 

 

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Hook Questions:

1.    How do you graph a function?

2.    Are quadratic equations functions?

3.    How do you solve an equation graphically?

 

 

 

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