1. Jeff Bivin -- LZHS Quadratic Equations

2. Jeff Bivin -- LZHS Convert to Standard Form f(x) = 5x 2 - 40x + 46 f(x) = 5(x 2 - 8x + (-4) 2 ) + 46 - 60 f(x) = 5(x - 4) 2 - 14 Axis of symmetry: x = 4 Vertex: (4, -14) 5(-4) 2 = 60 x - 4 = 0 x = 4

3. Jeff Bivin -- LZHS Convert to Standard Form

4. Jeff Bivin -- LZHS Find the Axis of Symmetry & Vertex f(x) = 5x 2 - 40x + 46 Axis of symmetry: x = 4 Vertex: (4, -14)

5. Jeff Bivin -- LZHS To help graph – find the x-intercepts f(x) = 5x 2 - 40x + 46 = 0 Factor if possible --- if it doesn’t factor use the Quadratic Formula.

6. Jeff Bivin -- LZHS Now we can graph it! axis of symmetry: x = 4 vertex: (4, -14) x-intercepts: (6.608, 0)(1.392, 0)

7. Jeff Bivin -- LZHS Write the Equation in Standard Form Vertex: (3,5)Passes through: (1, -2)

8. Jeff Bivin -- LZHS Write the Equation in Standard Form x-intercepts: (-5, 0) and (3, 0) f(x) = a (x + 5)(x - 3) If the parabola opens up, chose a positive “a” value. If the parabola opens down, chose a negative “a” value. f(x) = 4 (x + 5)(x - 3) Let’s choose a = 4 f(x) = 4 (x 2 + 2x - 15) f(x) = 4x 2 + 8x - 60 f(x) = -7 (x + 5)(x - 3) Let’s choose a = -7 f(x) = -7 (x 2 + 2x - 15) f(x) = -7x 2 - 14x + 105

9. Jeff Bivin -- LZHS Find two positive real numbers whose product is a maximum and whose sum is 90. The two numbers are 45 and 45.

10. Jeff Bivin -- LZHS Find two positive real numbers whose product is a maximum and whose sum of the first number and twice the second number is 32. The two numbers are 16 and 8.