Quiz review Direction of Opening Y – intercept Vertex AOS Min/Max Value Number of solutions Solutions Domain and Range Increasing Decreasing

Quiz Review

On the Calculator On the Calculator: Min/Max (Vertex) AOS Zeros **Put equation in y1 **Hit 2nd Trace **Follow directions on Calculator

Properties of quadratic equations - equation September 26th

Standard form of quadratic equations y = ax2 + bx + c a ≠ 0

What does the equation of a quadratic function tell us? Let’s look at y = x2 and y = -x2: Think-Pair-Share: What do you notice about these two graphs? What is the difference between the two equations? What do you think the difference means? Parabola

What does the equation of a quadratic function tell us? Direction of opening: If a>0, the direction of opening is UP. If a<0, the direction of opening is DOWN. Example: y = 5x2 + 10x – 7

What does the equation of a quadratic function tell us? Graph the equation in you calculator: y = x2 + 4x – 5 What is the y – intercept?

What does the equation of a quadratic function tell us? y – intercept: In standard form, c gives us the y-intercept: y = ax2 + bx + c Example: y = 5x2 + 10x – 7

What is the direction of opening and y – intercept of the equations? 1. y = -8x2 + 2x + 1 2. y = 6x2 – 24x - 4

What does the equation of a quadratic function tell us? Axis of Symmetry (AOS): we can use the formula to find the AOS. Example: y = -x2 + 8x + 16

What does the equation of a quadratic function tell us? Vertex: plug the AOS in for x and find the y value of the vertex. Example: y = -x2 + 8x + 16

Find the AOS and vertex y = -8x2 + 2x + 1 y = 6x2 – 24x - 4

What does the equation of a quadratic function tell us? Maximum/Minimum: highest/lowest point If a < 0, the graph has a ______________ If a > 0, the graph has a ______________ The maximum/minimum value is the y – value of the vertex. Example: y = -x2 + 8x + 16

Properties – Practice using the equation 1. y = x2 + 6x + 8 Direction of Opening: y – intercept: AOS: Vertex: Max or Min Value:

Warm up -x2 + 10x + 25 2x2 – 4x – 6 Direction of Opening? For the two quadratics answer these questions: Direction of Opening? Y – intercept? AOS? Vertex?

Properties – Review using the equation y = -2x2 + 12x + 16 Direction of Opening: y – intercept: AOS: Vertex: Max or Min Value: Sketch the Graph:

Properties – Review using the equation y = 2x2 + 24x + 20 Direction of Opening: y – intercept: AOS: Vertex: Max or Min Value: Sketch the Graph:

Activity You and your partner will either have a picture of a graph or the equation of the graph. You should take a couple minutes to right down everything you know about your graph/equation. Then when I say, walk around the room and find the pair with the matching graph/equation. Example: Matching Graph to Equation

Flex - Factoring Review Factor the following expressions: x2 – 15x + 50: (x – 5)(x – 10) 12xy – 4y + 9x – 3: (4y + 3)(3x – 1) x2y - 3x2 – 8y - 24: (x2 – 8)(y – 3) x2 – 36: (x – 6)(x + 6) 20x2 – 16x: 4x(5x – 4) 4x2 - 24x + 36: 4(x – 3)(x – 3) 2x3 + 12x2 + 16x: 2x(x + 4)(x + 2) x2 - 5x - 14: (x – 7)(x + 2) 15ab – 5b + 9a – 3: (5b – 3)(3a – 1)

Zeros, roots, x – intercepts, solutions Remember: factor the equation then set each set of parentheses equal to 0 and solve for x. Example (solve by factoring): y = 3x2 + 2x – 5

You try (x + 5)(x – 1) = 0 (2y – 1)(3y + 2) = 0 (3x – 3)(4x – 8) = 0 (7n – 14)(6n – 3) = 0

Solve by factoring 1. y = x2 - 10x - 11 2. y = -3x2 + 12

Solve by factoring 3. y = -2x2 + 6x + 56 4. y = 4x2 - 8x - 32

Solve by factoring 5. y = 3x2 – 9x 6. y = 3x2 + 4x – 4

Stations Review Complete All Stations – Due at the end of class time!

Homework Worksheet