Chapter 5 – Quadratic Functions and Factoring 5.2 – Graphing Quadratic Functions in Vertex or Intercept Form

5.2 – Graphing Quadratic Functions in Vertex or Intercept Form Today we will learn how to: Graph quadratic functions in different forms

5.2 – Graphing Quadratic Functions in Vertex or Intercept Form Quadratic functions can be written in different forms; vertex form and intercept form. Vertex form y = a(x – h)2 + k When a > 0, the parabola opens up When a < 0, the parabola opens down

5.2 – Graphing Quadratic Functions in Vertex or Intercept Form Steps for Graphing y = a(x – h)2 + k Draw the axis of symmetry (x = h) Plot the vertex (h, k) Plot two other points on one side of the vertex. Use symmetry to mirror the points. Draw the parabola.

5.2 – Graphing Quadratic Functions in Vertex or Intercept Form Example 1 Graph y = ½(x – 3)2 – 5

5.2 – Graphing Quadratic Functions in Vertex or Intercept Form Example 2 Graph the equation y = -2(x + 2)2 + 4

5.2 – Graphing Quadratic Functions in Vertex or Intercept Form Example 3 Graph the equation y = (x – 2)2

5.2 – Graphing Quadratic Functions in Vertex or Intercept Form HOMEWORK 5.2 Practice A Worksheet #1 – 9

5.2 – Graphing Quadratic Functions in Vertex or Intercept Form The other form in which a quadratic equation can be written is intercept form. Intercept Form y = a(x – p)(x – q) When a > 0, the parabola opens up When a < 0, the parabola opens down It will contain the points (p, 0) and (q, 0)

5.2 – Graphing Quadratic Functions in Vertex or Intercept Form Steps for Graphing y = a( x – p)(x – q) Draw the axis of symmetry. It’s the line x = (p + q)/2 Find and plot the vertex. The x-value is (p + q)/2. Substitute the value for x and solve for y Plot the points where the x-intercepts, p and q, occur. Draw a parabola.

5.2 – Graphing Quadratic Functions in Vertex or Intercept Form Example 4 Graph y = (x + 2)(x – 4)

5.2 – Graphing Quadratic Functions in Vertex or Intercept Form Example 5 Graph y = -2(x – 1)(x – 2)

5.2 – Graphing Quadratic Functions in Vertex or Intercept Form Example 6 Graph y = ½ (x + 4)(x – 2)

5.2 – Graphing Quadratic Functions in Vertex or Intercept Form Minimum and Maximum Values In any of the three forms of a quadratic function, the value of a tells you whether the parabola opens up or down. When a > 0, the y-coordinate of the vertex is the minimum value of the function When a < 0, the y-coordinate of the vertex is the maximum value of the function

5.2 – Graphing Quadratic Functions in Vertex or Intercept Form Example 7 Tell whether function y = 3(x – 3)(x + 2) has a minimum value or a maximum value. Then find the value.

5.2 – Graphing Quadratic Functions in Vertex or Intercept Form Example 8 Tell whether function y = -5(x + 9)(x – 4) has a minimum value or a maximum value. Then find the value.

5.2 – Graphing Quadratic Functions in Vertex or Intercept Form Example 9 The Golden Gate Bridge in San Francisco, CA has two towers. The top of each tower is 500 feet above the road. The towers are connected by suspension cables. Each cable forms a parabola with the equation where x and y are measured in feet.

5.2 – Graphing Quadratic Functions in Vertex or Intercept Form Example 9 – cont. Find the height of the cable above the road, when the cable is at the lowest point. The road is represented by y = 0 What is the distance between the towers?

5.2 – Graphing Quadratic Functions in Vertex or Intercept Form Example 10 You kick a football. The path the football travels can be modeled by the graph of the function y = -0.026x(x – 46) where x is the horizontal distance (feet) and y is the height of the football (feet). In which form is the equation written? What is the horizontal distance that the football travels? What is the maximum height of the football?

5.2 – Graphing Quadratic Functions in Vertex or Intercept Form HOMEWORK 5.2 Worksheet #10 – 29