Unit 1B quadratics Day 4

Graphing a Quadratic Function M2 Unit 1B: Day 4 Lesson 3.1B EQ: How do we graph a quadratic function and identify all of its characteristics?

Today, we are going to begin by reviewing what we have learned about graphing quadratics so far Lets recall how to find the following: Vertex AOS Maximum or Minimum Y-intercept

Find: a) vertex b) axis of symmetry c) state whether the vertex is a maximum or minimum. d) y - intercept a = -2, b = 4 c = -2 4 a) Vertex: b) Axis of symmetry: c) Since a < 0, the parabola opens down and has a: maximum (1, 0) x = 1 d) y-intercept: (0, -2)

a = 1, b = 0 c = 2 5 Find: a) vertex b)axis of symmetry c) state whether the vertex is a maximum or minimum. d) y-intercept a) Vertex: b) Axis of symmetry: c) Since a > 0, the parabola opens up and has a: minimum (0, 2) x = 0 d) y-intercept: (0, 2)

a = -3 h = 1 k = 2 a) Vertex: b) Axis of symmetry: c) Since a < 0, the parabola opens down and has a: maximum 6 Find: a) vertex b) axis of symmetry c) state whether the graph has a maximum or minimum. d) y - intercept (1, 2) x = 1 d) y-intercept: (0, -1)

Domain VS. Range Domain: (x – values) read domain from left to right Range: (y-values) read range from bottom to top

Last week we said that the DOMAIN of parabolas is all real numbers…unless the parabola looks like this and has endpoint(s) 8 We say the domain is restricted, therefore it is no longer all real numbers

Find the domain of the graph below Domain: 9 -1 < x < 2

Find the domain of the graph below Domain: < x < 2

Find the domain of the graph below Domain: 11

Vertex: Y-intercept: Axis of symmetry: One more point: Domain: Range: Max or Min? Graph the quadratic using the axis of symmetry and vertex. maximum All real numbers y ≤ 3 12 Extrema:y = 3

Vertex: Y-intercept: Axis of symmetry: One more point: Domain: Range: Max or Min? Graph the quadratic using the axis of symmetry and vertex. minimum All real numbers y ≥ 0 13 (-1, 0) Extrema:y = 0

Vertex: Y-intercept: Axis of symmetry: One more point: Domain: Range: Max or Min? Graph the quadratic using the axis of symmetry and vertex. maximum All real numbers 14 Extrema:y = 5/4

Stretch VS. Shrink Compare the following graphs and equations: What is the difference between these two graphs when compared to the parent function? *note: rubber band Vertical stretch Vertical shrink

Look at a couple more… What we should notice and confirm at this point is that the value of “a” determines how wide or narrow the graph will be… When ‌ a ‌ is greater than 1, we call that a vertical stretch When ‌ a ‌ is less than 1, we call that a vertical shrink

State whether the graph shows a vertical stretch or vertical shrink Shrink…so |a| < 1 Stretch…so |a| > 1

18 Intervals of increase and decrease To determine the intervals of increase and decrease, you must “read” the graph from left to right What are these lines doing from left to right?

19 Let’s apply this idea to parabolas… To determine the intervals of increase and decrease, you must “read” the graph from LEFT to RIGHT What is this parabola doing on the left side of the vertex? Going downhill What is this parabola doing on the right side of the vertex? Going uphill Interval of decreaseInterval of increase

20 One more… What is this parabola doing on the left side of the vertex? Going uphill What is this parabola doing on the right side of the vertex? Going downhill Interval of decreaseInterval of increase

21 Graph each quadratic function and determine the interval of increase and decrease Interval of decrease Interval of increase y = -2x² + 12x - 14

22 Interval of decrease Interval of increase Graph each quadratic function and determine the interval of increase and decrease y = x² + 2x + 3

23 Interval of decrease Interval of increase Graph each quadratic function and determine the interval of increase and decrease

24 Determine if the given interval is an interval of increase or decrease decreaseincrease

25 Determine if the given interval is an interval of increase or decrease increase

26 Assignment: Day 2 Handout