Splash Screen
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Transcript of Splash Screen
You graphed linear equations by using tablesand finding roots, zeros, and intercepts.
• Solve linear equations by graphing.
• Estimate solutions to a linear equation by graphing.
Learning Goal
• linear function – a function for which the graph is a line
• parent function – the simplest of functions in a family
• family of graphs – graphs and equations of graphs that have at least one characteristic in common.
• root - the solutions of a quadratic equation
• zeros – The x-intercepts of the graph of a function; the values of x for which ƒ(x) = 0.
Vocabulary
Solve an Equation with One Root
A.
Answer: The solution is –6.
Subtract 3 from each side.
Original equation
Multiply each side by 2.
Simplify.
Method 1 Solve algebraically.
!!!! Change ƒ(x) to 0 !!!!
Solve an Equation with One Root
B.
Find the related function. Set the equation equal to 0.
Method 2 Solve by graphing.
Original equation
Simplify.
Subtract 2 from each side.
Solve an Equation with One Root
Answer: So, the solution is –3.
The graph intersects the x-axis at –3.
The related function is To graph the function, make a table.
Solve an Equation with No Solution
A. Solve 2x + 5 = 2x + 3.
Answer: Since f(x) is always equal to 2, this function has no solution.
2x + 2 = 2x Subtract 3 from each side.
2x + 5 = 2x + 3 Original equation
2 = 0 Subtract 2x from each side.
The related function is f(x) = 2.
The root of the linear equation is the value of x when f(x) = 0.
Method 1 Solve algebraically.
Solve an Equation with No Solution
B. Solve 5x – 7 = 5x + 2.
Answer: Therefore, there is nosolution.
5x – 9 = 5x Subtract 2 from each side.
5x – 7 = 5x + 2 Original equation
–9 = 0 Subtract 5x from each side.
Graph the related function, which is f(x) = –9. The graph of the line does not intersect the x-axis.
Method 2 Solve graphically.
A. x = 0
B. x = 1
C. x = –1
D. no solution
A. Solve –3x + 6 = 7 – 3x algebraically.
Remember to set the equation equal to 0.
Estimate by Graphing
FUNDRAISING Kendra’s class is selling greeting cards to raise money for new soccer equipment. They paid $115 for the cards, and they are selling each card for $1.75. The function y = 1.75x – 115 represents their profit y for selling x greeting cards. Find the zero of this function. Describe what this value means in this context.
The graph appears to intersect the x-axis at about 65. Next, solve algebraically to check.
Make a table of values.
Estimate by Graphing
Answer: The zero of this function is about 65.71. Since part of a greeting card cannot be sold, they must sell 66 greeting cards to make a profit.
0 = 1.75x – 115 Replace y with 0.
y = 1.75x – 115 Original equation
115 = 1.75x Add 115 to each side.
65.71 ≈ x Divide each side by 1.75.