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Standard Forms of Varies Functions
Warm-Up
1. Write the standard forms for a linear
equation, quadratic equation, and an
exponential function.
2. Find the minimum point of the function
f(x) = 4x2 + 2x - 6
3. What is the parent function of the function
f(x)= 6x + 9
4. What translation occurs to the parent
function of the function g(x) = (x-2)2 + 3?
1. Write the standard forms for a linear
equation, quadratic equation, and an
exponential function.
linear: f(x) = mx+b
quadratic equation: f(x) = ax2 + bx + c
exponential : f(x) = a*bx
2. Find the minimum point of the function
f(x) = 4x2 + 2x - 6
(0,-6)
3. What is the parent function of the function
f(x)= 6x + 9
f(x) = x
4. What translation occurs to the parent
function of the function g(x) = (x-2)2 + 3?
The function will move up 3 units and over to
the right 2 units.
Objective
Graphical Behaviors p. 45
Classwork
Do pages 47 – 59.
p. 43
Rewrite Equations and Formulas
OBJ: To recognize and solve literal
equations; to rewrite equations and
formulas.
Literal Equation
• An equation with two or more variables.
• An equation in which letters are used to replace
coefficients and constants of another equation.
• Examples:
A  r
2
x1 x2  3  0
ax  b  c
P  2l  2 w
Solving Literal Equations
• Solving equations for one variable in terms of
the other variables without substituting any
values.
• Examples:
– Solve V =lwh for h.
– Solve A = p +prt for r.
– Solve A = p + prt for p.
**Use the same rules for solving equations. The only difference
is that it is not numbers, it is only variables.
Solve literal equations
• Solve ax + b = c for x. Then use the solution to
solve 2x + 5 = 11
• Step 1: Solve ax + b = c for x
• Step 2: Use the solution to solve
2x + 5 = 11.
• The solution of 2x + 5 = 11 is 3.
• Example: Solve p + qx = r for x. Then use the
solution to solve 3+5x = -7.
Two or more variables…
•
•
•
•
Write -2x + 3y = 6 so that y is a function of x.
This means solve for y.
Write 12 = 9x + 3y so that y is a function of x.
Write 14 = 7y – 6x so that y is a function of x.
Solve and use Geometric Formulas
• The area for a rectangle is given by the
formulas A = lw, where l is the length and w is
the width.
• Solve the formula for the length l.
• Use the rewritten formula to find the length of
this rectangle.
A = 351 cm2
13 cm
Homework
• Text p. 187- 188
– #’s 3-6, 12 – 18 evens, 20 -22, 24, 26, 27, 32, 33