Warm ups Graph completely (with all parts from worksheet)

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Presentation transcript:

Warm ups Graph completely (with all parts from worksheet)

11-2 Solving Quadratic Equations by Graphing Objective: To find the roots of a quadratic equation. Standard 21.0

Homework Questions? View Answer Key

Example 1 Let’s use the warm up problem! Look at where the parabola crosses the x axis… These points are the ROOTS! The roots are the x-intercepts. Look at your warmup graph… where does it cross the x axis?

Look at the roots.. How else did we learn how to solve these? Factoring!

What are the roots?

Roots can look like… 2 roots1 rootNo real roots

ROOTS FOR TOO #2 are like this Does not fall on a nice, whole number Between 2 numbers: write as inequality Start all the way to the left Write with “<“ signs “x” in the middle of the 2 #’s 2 < x < 3 6 < x < 7

TOO – BAD slide. Solve by graphing. Roots Estimate if not exact. If not sure if it is exact, then try to factor! Vertex in on x-axis Does not cross x-axis

Example 2 Graph given roots {-2,0} and minimum (-1,-1) Vertex!!

RECAP OF ROOTS 2 Roots Crosses x-axis twice Vertex is below and opens up Vertex is above and opens down Whole Numbers Answer: (x,0) and (x,0) Between 2 Numbers Answer: # < x < # # < x < # 1 Root Vertex is on the x-axis Answer is vertex! (x,0) No Roots Does not cross x-axis Vertex is above and opens up Vertex is below and opens down Answer: None

SIDE NOTE Y-intercept, x always equals 0 so... EX#1 y = 1/2x 2 – 2x + 2 y = 1/2(0) 2 – 2(0) + 2 y = 0 – y = 2 (0,2) y-intercept Y-intercept is ALWAYS “c” Ex: y = 2x 2 – 5x + 26 (0,26) EX #2 y = -x 2 – 2x + 3 y = -(0) 2 – 2(0) + 3 y = 0 – y = 3 (0,3) y-intercept

Homework Pg. 625 # 17-19, 20-23, Graph the parabola first, THEN see where it crosses the x-axis. The point(s) at which it crosses (once, twice, or none) are the roots. Write the roots in brackets { } Use graph paper!

Math Lab Warmup: Simplify

Simplify

Review Commonly missed test questions: factor.

Review Commonly missed test questions: factor.

Review Commonly missed test questions: solve

Review Commonly missed test questions: solve

Homework Groups Let’s get into the same homework groups that we worked on yesterday. Once you are seated, raise your hand if you are all finished, or finish, your homework.

If you finish homework.. Either graph or solve using quad. Formula: Depending on what you’ve learned so far