9.4 – Solving Quadratic Equations BY GRAPHING!. Warm-Up.

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Presentation transcript:

9.4 – Solving Quadratic Equations BY GRAPHING!

Warm-Up

What is a Quadratic Equation? A quadratic equation in standard form is written: y = ax 2 + bx + c, where a ≠ 0

Roots of a Quadratic Equation roots solutions The roots of a quadratic equation are the solutions to: 0 = ax 2 + bx + c Quadratic equation in standard form with y = 0 What kind of points on a graph have y- values of 0? Where do we find these points? What might we call them?

Roots of a Quadratic Equation Roots are represented graphically by the x- intercepts of the graph of a quadratic equation. Roots Roots, Roots, Baby!

Connecting Solutions to Roots

x = 2, -2

Quick Practice!

So how does this help me?

I GET IT NOW!!!

Getting it Done by Hand Solve the following equation by graphing (you may not use any graphing technology): x012 y

Steps to graph a quadratic equation: 1.Put equation into standard form. 2.Replace the 0 with y. 3.Graph the function on your calculator using the Y= button. 4.Find the zeros using the “CALC” menu ( 2 nd TRACE ), setting left and right boundaries and making a guess. 5.Check answers! Graph: 4x 2 = 16 Using a Calculator

Graph: x 2 - 4x = 5 Steps to graph a quadratic equation: 1.Put equation into standard form. 2.Replace the 0 with y. 3.Graph the function on your calculator using the Y= button. 4.Find the zeros using the “CALC” menu ( 2 nd TRACE ), setting left and right boundaries and making a guess. 5.Check answers!

Using a Calculator Graph: x 2 = -x + 6 Steps to graph a quadratic equation: 1.Put equation into standard form. 2.Replace the 0 with y. 3.Graph the function on your calculator using the Y= button. 4.Find the zeros using the “CALC” menu ( 2 nd TRACE ), setting left and right boundaries and making a guess. 5.Check answers!

Using a Calculator Graph: Make one up! Steps to graph a quadratic equation: 1.Put equation into standard form. 2.Replace the 0 with y. 3.Graph the function on your calculator using the Y= button. 4.Find the zeros using the “CALC” menu ( 2 nd TRACE ), setting left and right boundaries and making a guess. 5.Check answers!

A baseball is thrown at 100 mph ft/sec from left field toward home plate. The models below give paths of the ball for two initial angles, with height of y and horizontal distance x (both measure in feet) If home plate is 236 feet away, which angle(s) have the ball hitting the ground before reaching the plate?

Homework Complete worksheet by tomorrow! Quiz on Monday 5/6!