quick write write down the 2 formats we have learned for quadratics under each format, write down...
TRANSCRIPT
Quick Write
• Write down the 2 formats we have learned for quadratics
• Under each format, write down all the things you can get from that format.
Review
• Multiply these together:
( 6)( 4)x x 2 2 24x x
INTERCEPT FORMAT
Section 4-2
Objectives
• I can find the solutions, axis of symmetry, and vertex point from Intercept Format
• I can graph a quadratic from Intercept Format
• I can convert Intercept Format to Standard Format
Intercept Format
( )( )y a x p x q p and q are the x-intercepts
AOS:2
p qx
a > 0 Opens Up
a < 0 Opens Down
Graphing Steps
• Find p and q
• Calculate AOS
• Calculate Vertex using AOS x-value
• Calculate y-intercept Let x = 0
2
p qx
EXAMPLE 3 Graph a quadratic function in intercept form
Graph y = 2(x + 3) (x – 1).
SOLUTION
STEP 1 Identify the x - intercepts. Because p = – 3 and q = 1, the x - intercepts occur at the points (– 3, 0) and (1, 0).
STEP 2 Find the coordinates of the vertex.
x = p + q2
– 3 + 1 2
= – 1=
y = 2(– 1 + 3)(– 1 – 1) = – 8
EXAMPLE 3 Graph a quadratic function in intercept form
STEP 3 Draw a parabola through the vertex and the points where the x - intercepts occur.
GUIDED PRACTICE
Graph the function. Label the vertex, axis of symmetry, and x - intercepts.
5. y = (x – 3) (x – 7)
SOLUTION
STEP 1 Identify the x - intercepts. Because p = 3 and q = 7, the x - intercepts occur at the points (3, 0) and (7, 0).
STEP 2 Find the coordinates of the vertex.
x = p + q2
3 + 7 2
= 5=
y = (5 – 3) (5 – 7) = – 4
So the vertex is (5, – 4)
GUIDED PRACTICE for Examples 3 and 4
STEP 3 Draw a parabola through the vertex and the points where the x - intercepts occur.
GUIDED PRACTICE for Examples 3 and 4
7. y = – (x + 1) (x – 5)
SOLUTION
STEP 1 Identify the x - intercepts. Because p = – 1 and q = 5, the x - intercepts occur at the points (– 1, 0) and (5, 0).
STEP 2 Find the coordinates of the vertex.
x = p + q2
– 1 + 5 2
= 2=
y = – (2 + 3)(2 – 1) = 9
So the vertex is (2, 9)
GUIDED PRACTICE for Examples 3 and 4
STEP 3 Draw a parabola through the vertex and the points where the x - intercepts occur.
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) Write original function.
= – 2 (x2 – 8x + 5x – 40) Multiply using FOIL.
= – 2 (x2 – 3x – 40) Combine like terms.
= – 2x2 + 6x + 80 Distributive property
GUIDED PRACTICE for Examples 5 and 6
Write the quadratic function in standard form.9. y = – (x – 2) (x – 7)
y = – (x – 2) (x – 7) Write original function.
= – (x2 – 7x – 2x + 14) Multiply using FOIL.
= – (x2 – 9x + 14) Combine like terms.
= – x2 + 9x – 14 Distributive property
GUIDED PRACTICE for Examples 5 and 6
12. y = – 7(x – 6) (x + 1)
y = – 7(x – 6) (x + 1) Write original function.
= – 7(x2 + x – 6x – 6) Multiply using FOIL.
= – 7(x2 – 5x – 6) Combine like terms.
= – 7x2 + 35x + 42 Distributive property