1. Graph each function. Label the vertex and axis of symmetry.
4.2
WARM-UP
Graph each function. Label the vertex and axis of symmetry.
y = 5x2
y = 4x2 + 1
y = -2x2 – 6x + 3
Vertex is (0,0).
Axis of symmetry is x = 0.
Vertex is (0,1).
Axis of symmetry is x = 0.
Vertex is (-1.5,7.5).
Axis of symmetry is x = -1.5.

3. Graph Quadratic Functions in Vertex or Intercept Form
4.2
Graph Quadratic Functions in Vertex or Intercept Form
In the previous lesson we graphed quadratic functions in Standard Form: y = ax2 + bx + c, a ≠ 0
Today we will learn how to graph quadratic functions in two more forms:
Vertex Form
Intercept Form

4. Vertex Form (h, k) (h, k) Graph Vertex Form: y = a (x – h)2 + k And
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Characteristics of the graph of: y = a (x – h)2 + k
y = a (x – h)2 + k
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1. The graph is a parabola with vertex (h, k).
(h, k)
y = x2
(h, k)
2. The axis of symmetry is x = h
x = h Axis of symmetry
3. The graph opens up if a > 0 and opens down if a < 0.

5. Opens down a < 0. (-1 < 0)
GUIDED PRACTICE
Graph the function. Label the vertex and axis of symmetry.
2. y = (x + 2)2 – 3
Vertex (h, k) = (– 2, – 3).
Axis of symmetry is x = – 2.
3. y = – (x + 1)2 + 5
Vertex (h, k) = (– 1, 5).
Axis of symmetry is x = – 1.
Opens down a < 0. (-1 < 0)

6. GUIDED PRACTICE 12 4. f (x) = (x – 3)2 – 4 Vertex (h, k) = ( 3, – 4).
Axis of symmetry is x = 3.
Opens up a > 0. (1/2 < 0)

7. Intercept Form y = a (x – p) (x – q)
Graph Intercept Form: y = a (x – p) (x – q)
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Characteristics of the graph of y = a (x – p) (x – q):
x = (p + q) / 2
1. The x – intercepts are p and q, so the points (p, 0) and (q, 0) are on the graph.
y = a (x – p) (x – q)
2. The axis of symmetry is halfway between (p, 0) and (q, 0) and has equation: x = (p + q) / 2
(q, 0)
(p, 0)
3. The graph opens up if a > 0 and opens down if a < 0.

8. Graph the function. 6. y = (x – 3) (x – 7) 7. f (x) = 2(x – 4) (x + 1)
x - intercepts occur at the points (3, 0) and (7, 0).
Axis of symmetry is x = 5
Vertex is (5, – 4).
f (x) = 2(x – 4) (x + 1)
x - intercepts occur at the points (4, 0) and (– 1, 0).
Axis of symmetry is x = 3/2.
Vertex is (3/2, 25/2).

9. x - intercepts occur at the points (– 1, 0) and (5, 0).
GUIDED PRACTICE
y = – (x + 1) (x – 5)
x - intercepts occur at the points (– 1, 0) and (5, 0).
Vertex is (2, 9).
Axis of symmetry is x = 2.

10. Changing quadratic functions from intercept form or vertex form to standard form.
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.
Example:
F O I L
(x + 4)(x + 7) = x2 + 7x + 4x + 28
= x2 + 11x + 28

11. EXAMPLE 5
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

12. EXAMPLE 6
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
= 4x2 – 8x + 13

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

14. Homework: p. 249: 3-52 (EOP) GUIDED PRACTICE 9. y = – 3(x + 5)2 – 1
= – 3(x + 5) (x + 5) – 1
= – 3(x2 + 5x + 5x + 25) – 1
= – 3(x2 + 10x + 25) – 1
= – 3x2 – 30x – 75 – 1
= – 3x2 – 30x – 76
Homework: p. 249: 3-52 (EOP)