VERTEX Form of Quadratic Functions Math 2 Y















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VERTEX Form of Quadratic Functions Math 2 Y

Vertex Form: • 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 a quadratic function in vertex form Graph y = – 1 (x + 2)2 + 5. 4 SOLUTION STEP 1 Identify the constants a = – 1 , h = – 2, and k = 5. 4 Because a < 0, the parabola opens down. STEP 2 Plot the 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 symmetry. STEP 4 Draw a parabola through 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(x 2 – 8 x + 5 x – 40) – 2(x 2 – 3 x – 40) – 2 x 2 + 6 x + 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) + 9 4(x 2 – x + 1) + 9 4(x 2 – 2 x + 1) + 9 4 x 2 – 8 x + 4 + 9 4 x 2 – 8 x + 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 –x 2 + 9 x – 14 8. y = – 4(x – 1)(x + 3) ANSWER – 4 x 2 – 8 x + 12

GUIDED PRACTICE Write the quadratic function in standard form. 9. y = – 3(x + 5)2 – 1 ANSWER – 3 x 2 – 30 x – 76 10. g(x) = 6(x – 4)2 – 10 ANSWER 6 x 2 – 48 x + 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)
Quadratic functions: vertex form assignment
Quadratic function examples with answers
How to write in vertex form
How to find vertex of a quadratic function
Vertex form of a cubic function
Finding the vertex of a parabola
Standard form graphing
In vertex form
Standard form to vertex form
Intercept form
General form to vertex form
Vertex form
Properties of quadratic functions
Vertex form
Properties of quadratic function
Standard form of a quadratic function