# Unit 1B quadratics Day 3. Graphing a Quadratic Function EQ: How do we graph a quadratic function that is in vertex form? M2 Unit 1B: Day 3 Lesson 3.1B.

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Graphing a Quadratic Function EQ: How do we graph a quadratic function that is in vertex form? M2 Unit 1B: Day 3 Lesson 3.1B

Vertex Form Tells us the direction in which the parabola opens Provide the coordinates of the vertex: (h, k) ** NOTE: Always change the sign of h

4 First, we must be able to identify a, h, and k in each quadratic function. a = 2h = 3k = 1a = -1h = -2k = -4

5 Name the vertex of each quadratic function and determine if the parabola opens up or down. a = -2h = 3k = 4a = 1h = -1k = 2 Vertex is (3,4) Parabola opens down Vertex is (-1,2) Parabola opens up Vertex is (-4,0) Parabola opens down Vertex is (0,0) Parabola opens up

To find the y-intercept, substitute zero for each x in the equation Course 3 Y-intercept of a Quadratic Functions Find the y-intercept for 6 Example 3

Y-intercept of a Quadratic Functions Find the y-intercept for 7 Example 4

Find the y-intercept of the given Quadratic Functions The y-intercept is -14 or (0, -14) The y-intercept is 3 or (0, 3)

In order to graph using vertex form: Find the axis of symmetry and sketch it. Find the vertex, then plot it. Find the y-intercept, then plot it and its “twin” or “mirror image” Find another point and its “mirror image” 9

Extrema – y-coordinate of the vertex Maximum – the Vertex when the parabola opens down Minimum – the vertex when the parabola opens up minimum maximum 10

Vertex: (1, 3) Y-intercept: One more point: Graph the quadratic using the axis of symmetry and vertex. Minimum at y = 3 11 h = 1k = 3a = 2 Opens UP Axis of symmetry: (0, 5) (3, 11)

12 Vertex: (-1, -1) Y-intercept: One more point: Graph the quadratic using the axis of symmetry and vertex. Maximum at y = -1 h = -1k = -1a = -1 Opens DOWN Axis of symmetry: (0, -2) (1, -5)

13 Vertex: (2, 0) Y-intercept: One more point: Graph the quadratic using the axis of symmetry and vertex. Minimum at y = 0 h = 2k = 0a = 1 Opens UP Axis of symmetry: (0, 4) (1, 1)

14 Vertex: (-3, -2) Y-intercept: One more point: Graph the quadratic using the axis of symmetry and vertex. Maximum at y = -2 h = -3k = -2a = -1 Opens DOWN Axis of symmetry: (0, -11) (-2, -3)

Ex7. How would you translate the graph of to produce the graph of ? *Focus on how the vertex shifts! Old vertex: (0, 0) New vertex: (-2, -1) Translate left 2 units and down 1 unit.

9. How would you translate the graph of to produce the graph of ? Old vertex: (0, 0) New vertex: (1, 5) Translate right 1unit and up 5 units.

Domain The domain of a function is the set of all possible input values, x, which yield an output f(x) 17 x y MM2A3 Students will analyze quadratic functions in the forms f(x) = ax 2 +bx + c and f(x) = a(x – h) 2 = k. Range The range of a function is the corresponding set of output values, y.

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

Find the domain and range of the quadratic Function. f(x) = x 2 + 1 Domain: all real numbers Range: y ≥ 1 (the set of all real numbers greater than or equal to 1) 19

Domain of all parabolas is all real numbers… 20

Find the domain and range of the quadratic Function. f(x) = (x - 2) 2 + 5 Domain: all real numbers Range: y ≤ 5 (the set of all real numbers less than or equal to 5) 21

Find the domain and range of the quadratic Function. f(x) = - (x + 2) 2 - 1 Domain: all real numbers Range: y ≥ -1 22

Assignment 3.2 Practice WS (#1-12 all)

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