Unit 1B Quadratics Day 2

Graphing a Quadratic Function EQ: How do we graph a quadratic function in standard form? M2 Unit 1B: Day 2 Lesson 3.1A

Vocabulary Quadratic function Parabola Vertex Axis of Symmetry 3

A quadratic function contains a variable that is squared. In the quadratic function the y-intercept is c. The graphs of all quadratic functions have the same basic shape, called a parabola. If a > 0, the parabola opens up. If a < 0, the parabola opens down. f(x) = ax 2 + bx + c Course 3 Quadratic Functions 4

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If the parabola opens up, the lowest point is called the vertex (a > 0). 10 Quadratic Functions The graph of a quadratic function is a parabola. A parabola can open up or down. If the parabola opens down, the vertex is the highest point (a < 0). Vertex

1. f(x) = x 2 – x + 1 Plot the points and connect them with a smooth curve. x f(x) = x 2 – x + 1 –2–2 –1– (–2) 2 – (–2) + 1 = 7 (–1) 2 – (–1) + 1 = 3 (0) 2 – (0) + 1 = 1 (1) 2 – (1) + 1 = 1 (2) 2 – (2) + 1 = 3 Graph the following Create a table for each quadratic function, and use it to make a graph. 11

Create a table for each quadratic function, and use it to make a graph. 2. f(x) = x xf(x) = x –2–2 –1– (–2) = 5 (–1) = 2 (0) = 1 (1) = 2 (2) = 5 Graph the following 12

13 Now that we know standard form, we can name a, b, and c in each function a = 3, b = -2 c = 5 a = 3, b = 0 c = -1 a = -1, b = -5 c = 0 a = 0, b = 0 c = -51

14 The VERTEX of a parabola is the maximum or the minimum point. We now know that a parabola is defined by the equation VERTEX

How to find the vertex when the equation is in standard form… First, find the x-coordinate of the vertex using: Once you have x, then plug it in to find y

16 The AXIS OF SYMMETRY (AOS) of a parabola is a vertical line that goes through the vertex. How would you find the axis of symmetry? Since the AOS goes through the vertex and is a vertical line, it is the line AXIS OF SYMMETRY

17 WATCH HOW IT WORKS… a = -2, b = 4 c = 1 Vertex (1,3) Axis of symmetry x = 1. Since a < 0, the parabola opens down.

18 Now let’s try one together: Find: a) vertex b) axis of symmetry c) state whether it will open up or down a = 1, b = -6 c = 9 a) Vertex (3,0) b) Axis of symmetry x = 3. c) Since a > 0, the parabola opens up.

19 a = 1, b = 0 c = -16 a) Vertex (0,-16) b) Axis of symmetry x = 0. c) Since a > 0, the parabola opens up. Now you try one: Find: a) vertex b) axis of symmetry c) state whether it will open up or down

20 a = -3, b = 0 c = 2 a) Vertex (0,2) b) Axis of symmetry x = 0. c) Since a < 0, the parabola opens down. Try one more: Find: a) vertex b) axis of symmetry c) state whether it will open up or down

21 a = -13, b = 0 c = 0 a) Vertex (0,0) b) Axis of symmetry x = 0. c) Since a < 0, the parabola opens down. What about this one? Find: a) vertex b) axis of symmetry c) state whether it will open up or down

Summary Questions What is the equation for a quadratic function? f(x) = ax 2 + bx + c Parabola What do we call the graph of a quadratic function? How do we find the vertex of a quadratic function? Use to find the x-coordinate, then use this value and substitute into the equation to find the y -coordinate How do we find the axis of symmetry for a quadratic function? 22

Homework: Lesson 3.1 Practice WS (#1-13 all) 23