Section 4 2 Graph Quadratic Functions in Vertex

Section 4. 2: Graph Quadratic Functions in Vertex or Intercept Form

Vertex form – an equation in the form y = a(x – h)2 + k.

Graph of Vertex Form y = a(x – h)2 + k The graph of y = a(x – h)2 + k is the parabola y = ax 2 translated horizontally h units and vertically k units. Characteristics of the graph of y = a(x – h)2 + k • The vertex is (h, k). • The axis of symmetry is x = h. • The graph opens up if a > 0 and down if a < 0.

Example 1: Graph y = ½(x – 3)2 – 5 Label the vertex and axis of symmetry.

Example 2: Graph y = -(x – 1)2 + 5

HOMEWORK (Day 1) pg. 249; 4 – 9

If the graph of a quadratic function has at least one x-intercept, then the function can be represented in intercept form, y = a(x – p)(x – q). Characteristics of the graph of y = (x – p)(x – q) • The x-intercepts are p and q. • The axis of symmetry is halfway between (p, 0) and (q, 0). It has the equation. • The graph opens up if a > 0 and opens down if a < 0.

Example 3: Graph y = (x – 3)(x – 7). Label the vertex, axis of symmetry, and x-intercepts.

Example 4: Graph y = -(x + 1)(x – 5)

FOIL Method To multiply two expressions that each contain two terms, add the products of the First terms, the Outer terms, the Inner terms, and the Last terms. (x + 4)(x + 7) = x 2 + 11 x + 28

Example 5: Write the following in standard form. a) y = 3(x – 4)(x + 6) y = 3 x 2 + 6 x – 72 b) f(x) = - ½(x + 8)2 + 35 f(x) = - ½x 2 – 8 x + 3

Example 6: Find the minimum value or the maximum value of the function. a) y = 3(x – 3)2 – 4 minimum -4 b) g(x) = -5(x + 9)(x – 4) maximum 211. 25

HOMEWORK (Day 2) pg. 249; 13 – 16, 24 – 40 even