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Warm up

Warm up. Multiply by distribution the following polynomials 4(x 2 + 2x + 3) 2x( x 2 + 3x) 8(2x – 3). Quadratic Graphs. Vertex -Is the highest or lowest point on a parabola. Referred to as maximum for highest point and minimum for lowest point.

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Warm up

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  1. Warm up Multiply by distribution the following polynomials 4(x2 + 2x + 3) 2x( x2 + 3x) 8(2x – 3)

  2. Quadratic Graphs • Vertex-Is the highest or lowest point on a parabola. Referred to as maximum for highest point and minimum for lowest point. • Axis of symmetry-Is the vertical line that divides the parabola into two symmetric parts.

  3. Finding the axis of symmetry from the given quadratic equation • y = ax2 + bx + c • axis of symmetry • y = x2 – 2x – 3 y = 2x2 – 4x - 1

  4. Finding the vertex of a quadratic equation • once the axis of symmetry is found substitute what x is equal to into the quadratic equation to find y. • y = x2 – 2x – 3 y = 2x2 – 4x - 1

  5. Graphing Quadratic Functions • Positive – open up • F(x) = x2 + 4x + 3 • Negative – Open down • F(x) = -x2 + 3x - 2

  6. Graphing Quadratic Functions • F(x) = ax2 + bx + c a value – the a value tells you slope for one point away from the vertex

  7. Another form of a quadratic function • Standard form • F(x) = ax2 + bx + c • Vertex form • F(x) = a(x – h)2 + k • (h, k) is the vertex of the quadratic

  8. What are the vertexes of the equations below? • F(x) = 2(x - 2)2 + 5 • F(x) = -3(x + 7)2 – 8 • F(x) = (x - 5)2 – 3

  9. Graphing a Quadratic Equation • 1) Find the axis of symmetry • 2) Find the vertex • 3)look at the a value and plot the slope once! • 4)plot the points and connect them with a smooth curve to form a parabola

  10. Graph the quadratic equation • y = x2 – 2x - 3

  11. Graph the quadratic equation • y = x2 + 2x - 5

  12. Multiplying by distriution • 3x (2x2 + 4x – 6) 2(4x2 – 3x + 2)

  13. Multiplying by foiling or box method • (2x – 6)( 3x + 4) (x + 4)(2x – 6)

  14. Factoring GCF • 4x2 + 8x + 12 12x3 + 6x2 + 18x

  15. Factor by grouping • 4x2 + 2x + 8x + 4 6x2 + 3x + 8x + 4

  16. Factoring by difference of squares • X2 – 100 x2 - 25

  17. Factoring trinomials • X2 + 6x + 8 x2 + 7x + 12

  18. Factoring trinomials • 2X2 + 8x + 8 3x2 + 10x + 8

  19. A ball is thrown and follows the path described by the function h(t) = -2t2 +11t +6, where h is the height of the ball and t is the time since the ball was released. c) What is the ball’s maximum height?

  20. A ball is thrown and follows the path described by the function h(t) = -2t2 +11t +6, where h is the height of the ball and t is the time since the ball was released. e) From what height was the ball thrown?

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