Today in Pre-Calculus Go over homework Notes: –Quadratic Functions Homework

Quadratic Functions Standard form: f(x) = ax 2 + bx + c Roots (zeroes or x-intercepts) are found by factoring or using quadratic formula Vertex form: f(x) = a (x – h) 2 +k Vertex of the parabola (h, k) Axis of symmetry: x = h

Quadratic Functions To convert from standard form to vertex form using algebra: Complete the square. Example: y = 2x x + 31 y = 2(x 2 + 8x) + 31 Factor a only from x 2 and x y = 2(x 2 + 8x + 16) Divide new b by 2 and square it, must also multiply by a and subtract to keep equation true. y = 2(x +4) 2 – 1 Factor and simplify Parabola with vertex (-4, -1) and axis of symmetry x = -4.

Practice Example: Use algebra to describe y = 3x 2 – 18x – 17 y = 3(x 2 – 6x) – 17 Factor a from x 2 and x y = 3(x 2 – 6x + 9) – 27 – 17 Divide new b by 2 and square it, must also multiply by a and subtract to keep equation true. y = 3(x – 3) 2 – 44 Factor and simplify Parabola with vertex (3, -44) and axis of symmetry x = 3.

Formulas for h and k Example: y = 2x x + 31 k = 31 – (2)(-4) 2 or k = 2(-4) 2 +16(-4) + 31 k = -1 Vertex: (-4, -1)

Practice Use the formulas to find the vertex of y = 3x 2 + 5x – 4

Example Write the equation for a parabola with a vertex (-1,2) that goes through (6,100). start with vertex form: y = a(x + 1) substitute point 100 = a(6 + 1) = 49a a = 2 y = 2(x + 1) 2 + 2

Homework Pg. 182: even, even