VERTEX Form of Quadratic Functions Math 2Y

VERTEX Form of Quadratic Functions Math 2Y

2 Vertex Form: f ( x ) a ( x h) k h moves the parabola horizontally k moves the parabola vertically a makes the parabola narrow or wide VERTEX (opposite h, k) Axis of Symmetry is x opposite h *Reminder* If a 0 (positive), parabola opens up If a 0 (negative), parabola opens down

EXAMPLE 1 Graph y –1 4 SOLUTION Graph a quadratic function in vertex form (x 2)2 5. STEP 1 Identify the constants 1a – , h – 2, and k 5. 4 Because a 0, the parabola STEP 2 opens Plot thedown. vertex (h, k) (– 2, 5) and draw the axis of symmetry x – 2.

EXAMPLE 1 Graph a quadratic function in vertex form STEP 3 Evaluate the function for two values of x. 1 – x 0: y (0 2)2 5 4 4 1 – x 2: y (2 2)2 5 1 4 Plot the points (0, 4) and (2, 1) and their reflections in the axis of Draw a parabola through STEP 4 symmetry. the plotted points.

GUIDED PRACTICE Graph the function. Label the vertex and axis of symmetry. 1. y (x 2)2 – 3 h k Vertex: ( , ) a Axis of symmetry: x

GUIDED PRACTICE 2. y –(x 1)2 5 h k Vertex: ( , ) a Axis of symmetry: x

GUIDED PRACTICE 3. f(x) 1 2 (x – 3)2 – 4 h k Vertex: ( , ) a Axis of symmetry: x

Writing in Standard Form Goal is to manipulate the numbers so that they are in the form f(x) ax² bx c *Reminder* Order of Operations: PEMDAS!! You will need to distribute monomials, binomials, and trinomials! Let’s look at some examples

EXAMPLE 3 Change from intercept form to standard form Write y –2(x 5)(x – 8) in standard form. y –2(x 5)(x – 8) –2(x2 – 8x 5x – 40) –2(x2 – 3x – 40) –2x2 6x 80 Write original function. Multiply by Distributing. Combine like terms. Distributive property

EXAMPLE 3 Change from vertex form to standard form Write f (x) 4(x – 1)2 9 in standard form. f (x) 4(x – 1)2 9 4(x – 1) (x – 1) 9 4(x2 – x – x 1) 9 4(x2 – 2x 1) 9 4x2 – 8x 4 9 4x2 – 8x 13 Write original function. Rewrite (x – 1)2. Multiply by Distributing. Combine like terms. Distributive property Combine like terms.

GUIDED PRACTICE Write the quadratic function in standard form. 7. y –(x – 2)(x – 7) ANSWER –x2 9x – 14 8. y – 4(x – 1)(x 3) ANSWER –4x2 – 8x 12

GUIDED PRACTICE Write the quadratic function in standard form. 9. y –3(x 5)2 – 1 ANSWER –3x2 – 30x – 76 10. g(x) 6(x – 4)2 – 10 ANSWER 6x2 – 48x 86

GUIDED PRACTICE Graph the function. Label the vertex, axis of symmetry, and zeros. 4. y (x – 3)(x – 7) Zeros: Vertex: ( , ) Axis of symmetry: x

GUIDED PRACTICE 5. f (x) 2(x – 4)(x 1) Zeros: Vertex: ( , ) Axis of symmetry: x

Assignment Textbook pg. 67 # 2-14 even, 20, 22, 28, 30 (You will be given 6 blank graphs for #12, 14, 20, 22)