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Review: Simplify

This review covers solving quadratic equations, understanding the shape of a quadratic function, determining the vertex, axis of symmetry, and x-intercepts, and graphing quadratic functions. Key concepts include the form of a quadratic function, direction of opening, vertex, and equation of the axis of symmetry.

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Review: Simplify

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  1. Review: Simplify

  2. Review Solve the equation 5) 6) 7)

  3. Solve the equation 8) 9)

  4. Chapter 8 Section 3 Quadratic Functions and Their Graphs

  5. What do you know? • 3x2 + 12x + 8 = 0 • What is the shape? • If – 3 is the leading coefficient, how does the shape change? • What is know about the x-intercepts?

  6. Graph of a Quadratic Function • f(x) = • Graph is a parabola • Vertex • Axis of symmetry

  7. Form: f(x) = a(x - h)2 + k • Opens - - • Vertex (h, k) • Axis of symmetry: x = h • Example: f(x) = -2(x – 3)2 + 8 • Opens • Vertex: (3, -8) • Axis of symmetry: x = 3

  8. Find • Direction of opening • Vertex • Equation of the axis of symmetry • x-intercept(s) • f(x) = • g(x) =

  9. Form: f(x) = ax2 + bx + c • Opens? • x coordinate of the vertex: • x intercepts: solve f(x) = 0 • y intercept: (0, c)

  10. Find • Direction of opening • Vertex • Equation of the axis of symmetry • x-intercept(s) c) f(x) = d) g(x) =

  11. How would you determine? • Graph has a maximum value or minimum value.

  12. Write the equation, same shape as f(x) = 2x2 but • Has the vertex at (5, 3) • Maximum = 4 at x = -2

  13. Summary • Quadratic Function • How the x intercepts relate to the equation • Shape • Vertex • x, y intercept • graph

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