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Unit 9: Quadratic Functions
Transcript of Unit 9: Quadratic Functions
What you know: Factoring Key Vocabulary Objective it to describe what a root is and how to find one give two binomials. Quadratic Function
Axis of Symmetry
Solutions Day 3: Factoring Multiply the following binomials
Multiply the Binomials Roots The roots of a quadratic function are where the graph touches the x axis. How to Find Roots (x+2)(x-6) = 0 Step 1: Set both sides equal to zero x+2 = 0 x-6=0 Step 2: Solve each equation -2 -2 +6 +6 x = -2 x = 6 The roots are -2 and 6. This means the graph crosses the x axis at -2 and 6. Try it on your own! (x+3)(x-7)=0 x+3=0 x-7=0 x = -3 x = 7 Roots are at -3 and 7. This means the graph crosses the x axis at -3 and 7. Practice 3x(2x+12)(2x-6)=0 (2x+3)(4x -2)=0 3x=0 2x+12=0 2x-6=0 x = 0, -6, 3 2x+3=0 4x-2=0 x= -1.5, .5 Try it on your own! A kicker punted a field goal with an equations of (4x+3)(6x-12)=0. How many feet away did the ball land? 4x+3=0 6x-12=0 x = -.75, 2 Try it on your own! (6x + 12)(3x+6)=0 6x+12=0 3x+6=0
x = 2 You do not have to write it two times since they share the same root. Means it only crosses the x axis at one point. Objective is to factor polynomials using Algebra tiles and Algebraic Methods. Factors are numbers you multiply together to get a larger number How we apply it now: Factoring is a process in order to separate an expression/equation into its component parts. Working Backwards (x+4)(x+3) x +4x+3x+12 2 x + 7x + 12 2 You add terms to get the middle coefficient but multiply terms to get the last numer. SO... x + 8x + 15 2 S F F P um actor actor roduct Factors of 15 are (15 and 1) and (3 and 5). 3 and 5 add up to 8, so those are the factors we need. (x+3)(x+5) Factor the Trinomial x + 4x -12 2 S F F P Step 1: Find the "inside" numbers Step 2: Write Out the Binomials. (x+6)(x-2) Factor the Binomial x -16 2 S F F P If there is no middle term, then the sum is 0. If the sum is 0, then the numbers are ALWAYS opposites (x+4)(x-4) x -6x +9 2 Try it on your own! x + 11x +28 2 x +11x +30 2 Try it on your own! Parabola A curved shape that has an axis of symmetry. Step 1: Factor out a common number Steps 6x +x -1 Notes Break 2x +9x +10 Try it on your own 4x +8x+3 Try it on your own Vertex Vocabulary Review David bounced a ball that matched the equation
. At how many feet did the ball first hit the floor and at how many feet did the ball land again? Objective is to factor trinomials with a leading coefficient higher than one.
(2x +1)(x-2) 2x -2x + 1x -2
2x -x -2 2 2 2x -x -2 Before we have factored polynomials with a leading coefficient of one. Today we will learn how to factor them with higher leading coefficients. 2 This means that at least one of the binomials with have a larger coefficient. Step 2: 'Move the front to the back"
This means that you multiply the front coefficient with the back constant. Step 3: Factor the Trinomial
Step 4: Divide each constant by the original leading coefficient Simplify the fraction, and move the denominator to the front. 3x + 8x - 16 6x + 10x + 4 2 2 2x -11x -6 2 x - 11x -12 2 x - 11x -12 2 S
P (x-12)(x+1) (x-12)(x+1) __________
2 2 (x-6)(x+1) __________
2 (x-6)(2x+1) 2 Step 1: Is there a common factor?
Step 4: Reduce and move to the front Step 3: Factor Step 2: Move the front to the back x +x -6 2 S
P (x+3)(x-2) (x+3)(x-2) _____
6 6 (x+1)(x-1) _____
2 3 (2x+1)(3x-1) 2 2 (2x+5)(x+2) (2x+1)(2x+3) Zeros Maximum Minimum Parabola Solutions Roots Quadratic Predictions Graph Interpretation Vocabulary Roots and Characteristics Start Objective is to apply the process of quadratic regression and apply skills to word problems. Roots or Solutions Vertex Parabola Quadratic Regression is just like linear regression with only one difference. Quadratic Regression