4­3 Factoring and Solving Quad Equations by Factoring (2 days).notebook
October 20 and 24, 2014
ANY HOMEWORK QUESTIONS?
4 Step Factoring Method (when "a" not equal to 1)
• Check for common factor (if so, factor it out)
• Check if first and last terms are perfect squares
• Multiply a and c together
ax2 + bx + c = 0 • Drop "a" from the equation
• Rewrite the new equation and factor
• Divide the two constants by "a". ­If the division yields an integer, divide the two numbers and simplify. ­If division yields a number with a decimal, SIMPLIFY THE FRACTION, and the DENOMINATOR becomes the coefficient in front of x. 1
4­3 Factoring and Solving Quad Equations by Factoring (2 days).notebook
October 20 and 24, 2014
Homework Assignment #31:
Page 1, Part A: #3­21 every 3rd problem; Page 1, Part B: #6­10, 24,25,27,28,31,32; Page 2, Part C: #12­28 even
Solutions are right next to each problem in the smaller print and slightly different font!
4.3 ­ Solving Quadratic Equations by Graphing and Factoring
• A zero of a function is a value of the input x that makes the output f(x) equal zero. • The zeros of a function are the x­intercepts. • Quadratic functions can have two zeros, as shown at right. • These zeros are always symmetric about the axis of symmetry.
ANY HOMEWORK QUESTIONS?
• The solution to a quadratic equation of the form ax2 + bx + c = 0 are roots. • The roots of an equation are the values of the variable that make the equation true. • Since zeros are x ­ intercepts, and x ­ intercept are when y = 0, The
Zeros, Roots, Intercepts, Big
Solutions, Factors are all Secret!!!!!! RELATED!!!!!
2
4­3 Factoring and Solving Quad Equations by Factoring (2 days).notebook
October 20 and 24, 2014
Reading Math
• Functions have zeros or x­intercepts.
• Equations have solutions or roots. 1. Find the zeros or roots of each function by factoring.
a.
b.
c.
d.
2a. Write a quadratic function in standard form with zeros 4 and ­7.
2b. Write a quadratic function in standard form with zeros 3 and 0.
Any object that is thrown or launched into the air, such as a baseball, basketball, or soccer ball, is a projectile. The general function that approximates the height h in feet of a projectile on Earth after t seconds is given.
Note that this model has limitations because it does not account for air resistance, wind, and other real­world factors.
PHYSICS!!!!!!
3
4­3 Factoring and Solving Quad Equations by Factoring (2 days).notebook
October 20 and 24, 2014
3. A golf ball is hit from ground level with an initial vertical velocity of 80 ft/s. After how many seconds will the ball hit the ground?
Homework Assignment #32:
p. 242: #49­55 odd, 59­63 odd, 69,70,71­75 odd,
91,95,96
Write the general projectile function.
2 + v t + h
h(t) = –16t
0
0
Substitute 80 for v
2 + 80t + 0 0 and 0 for h 0 . h(t) = –16t
The ball will hit the ground when its height is zero.
4