Lesson 13: 9-3 Solving Quadratic Equations by Graphing

Why do the x-intercepts give the solutions to the quadratic equations?
Can the exact solutions of quadratic equations be found by sketchig the graph?
When will the quadratic equation have exactly one real solution? no solution?

double root

A.REI.4 Solve quadratic equations in one variable
F.IF.7a Graph a linear and quadratic function and show intercepts, maxima and minima.

SAT questions related to solving quadratrics: 2-3-13,3-3-14,1-3-16,5-3-3,8-3-16,1-4-25; analyzing graphs: 3-4-12,8-3-11,8-4-19,6-3-11

The solutions of quadratic equations are called roots. All quadratic equations have two roots. When the parabola crosses the x-axis at two distinct points, the roots are real. When the vertex of the parabola is on the x-axis, the roots are double real root. When the parabola does not intersect the x-axis, the roots are imaginary.

Dorton Arena at the state fairgrounds in Raleigh, North Carolina, has a shape created by two intersecting parabolas. The shape of one of the parabolas can be modeled by y=-x^2 +127x, where x is the width of the parabola in feet, and y is the length of the parabola in feet. The x-intercepts of the graph of this function can be used to find the distance between the points where the parabola meets the ground.

Solutions found from the graph of an equation may appear to be exact. Check them in the original equation to be sure.

If students assume that the vertex of a parabola always has coordinates that are integers, then point out an example that has values of the vertex that is greater than one integer and less than another.

Practice: Exercises 1 -9

Exercises 41-44

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