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5.1 Graphing Quadratic Functions

5.1 Graphing Quadratic Functions. I can graph quadratic functions in standard form. I can graph quadratic functions in vertex form. I can graph quadratic functions in intercept form. . You NEED graph paper today ! . Quadratic function? .

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5.1 Graphing Quadratic Functions

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  1. 5.1Graphing Quadratic Functions I can graph quadratic functions in standard form. I can graph quadratic functions in vertex form. I can graph quadratic functions in intercept form. You NEED graph paper today!

  2. Quadratic function? • We’ve been working with functions in the form y = mx + b. • This was called a linear function because the graph was a straight line. • A quadratic function is the form: • y = ax2 + bx + c where a ≠ 0 • The graph of a quadratic function is: • A parabola What’s different between a linear function and a quadratic function?

  3. Quadratic Function in Standard form y = ax2 + bx + c • To find the vertex: • The x coordinate is • To find the y coordinate, plug x back into the original function • Vertex • Can either be the minimum of the parabola or the maximum of the parabola. • If a is positive… • The parabola goes up (like a cup) • If a is negative… • The parabola goes down (like a frown)

  4. Quadratic Functiony = ax2 + bx + c • Axis of symmetry • Parabolas are always symmetric. • Makes a vertical ‘imaginary’ line at the x coordinate of the vertex that cuts the parabola into equal halves.

  5. Standard Form: y = ax2 + bx + c Example 1: Graphing a Quadratic Function in standard form c= 6 b= -8 a= 2 • y = 2x2 – 8x + 6 • Vertex: • x = • x = • x = • x = 2 • y = 2(2)2 – 8(2) + 6 • y = 2(4) – 16 + 6 • y = 8 -10 • y = -2 (2, -2)

  6. y = 2(3)2 – 8(3) + 6 • y = 2(9) – 24 + 6 • y = 18 – 24 + 6 • y = 0 • (3, 0) • y = 2(4)2 – 8(4) + 6 • y = 2(16) – 32 + 6 • y = 32 – 32 + 6 • y = 6 • (4, 6) • Axis of Symmetry: • x = 2 • You also need two more points to be able to make the graph. • Choose x = 3 and x = 4 because they are right after the Axis of Symmetry

  7. Vertex: (2, -2) • Axis of Symmetry: • x = 2 • Points: • (3,0) • (4,6)

  8. Individual Practice on graphing quadratics in standard form • Pg 253 • 20-25 • List the vertex • Axis of symmetry • At least 2 extra points • You have 15 minutes to work on this section of problems. • I will do the next part of notes in 15 minutes.

  9. Quadratic function in vertex form • y = a(x – h)2 + k • Vertex: • (h,k) • Axis of Symmetry: • x = h • You still also need to find two more points to plot.

  10. Vertex Form: y = a(x – h)2 + k Example 2: Graphing a Quadratic Function in Vertex Form • y = -3(x + 1)2 + 2 • Vertex: • (-1,2) • Axis of Symmetry: • x = -1 • Points: • (0,-1) • (1,-10) • x = 0 • y = -3(0+1)2 + 2 • y = -3(1)2 + 2 • y = -3(1) + 2 • y = -3 + 2 • y = -1 • x = 1 • y = -3(1+1)2 + 2 • y = -3(2)2 + 2 • y = -3(4) + 2 • y = -12 + 2 • y = -10

  11. Vertex: • (-1,2) • Axis of Symmetry: • x = -1 • Points: • (0,-1) • (1,-10)

  12. Individual practice on graphing quadratics in vertex form • Pg. 253 • 26-31 • List the vertex • Axis of symmetry • At least 2 extra points • You have 15 minutes to work on this section of problems. • I will do the next part of notes in 15 minutes.

  13. Quadratic Functions in Intercept Form • y = a(x – p)(x – q) • The x-intercepts are p and q. • The axis of symmetry is halfway between p and q. • The vertex is found by plugging the axis of symmetry back in to the function and solve for y.

  14. Intercept Form: y = a(x – p)(x – q) Example 3: Graphing quadratics in intercept form • y = -(x + 2)(x - 4) • X-intercepts: • -2 and 4 • Axis of symmetry: • x = 1 • Vertex: • (1,9) • x = 1 • y = -(1+2)(1-4) • y = -(3)(-3) • y = -(-9) • y = 9

  15. X-intercepts: • -2 and 4 • Axis of symmetry: • x = 1 • Vertex: • (1,9)

  16. Individual practice on graphing quadratics in intercept form • Pg. 254 • 32-37 • List the vertex • Axis of symmetry • Intercepts

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