Algebra 1 Graphs Solutions Test – Free PDF

Contents

This algebra 1 graphs solutions test checks graphs as solution sets, linear-quadratic systems and exponential expressions in 45 minutes, with 8 questions for a total of 20 points.

This test has 8 questions worth 20 points in total and takes about 45 minutes. Decide which points are solutions, solve a system with a line and a parabola, and work with exponential graphs and exponent rules. Show your work for every question.

Test information

Grade: Algebra 1
Chapter: Graphs as Solution Sets, Linear-Quadratic Systems and Exponential Expressions
Common Core: A-REI.D.10, A-REI.C.7, F-IF.C.7e, A-SSE.B.3c
Time: 45 minutes
Total: 20 points (Question 1: 2 pts; Question 2: 2 pts; Question 3: 3 pts; Question 4: 3 pts; Question 5: 2 pts; Question 6: 3 pts; Question 7: 3 pts; Question 8: 2 pts)

Algebra 1 Graphs Solutions Test: questions 1–5

Question 1: Points on a graph (2 points)

The graph of \(y=x^{2}-5\) is a parabola.

Is \((-3,4)\) on the graph? Justify. (1 point)
Is \((2,1)\) on the graph? Justify. (1 point)

Question 2: Solutions on a line (2 points)

The line shown is the graph of \(y=-2x+3\).

A line with four plotted points.

Which of the points P, Q, R and S are solutions of the equation? (1 point)
Show by substitution that one of the other points is not a solution. (1 point)

Question 3: Line and parabola system (3 points)

Solve the system \(y=x^{2}-6x+8\) and \(y=2x-7\). Show all work.

Question 4: Reading a system graph (3 points)

The graph shows \(y=x^{2}-4\) (solid) and \(y=x-2\) (dashed).

A parabola and a line.

Estimate the coordinates of the intersection points from the graph. (1 point)
Verify them by solving the system algebraically. (2 points)

Question 5: How many solutions? (2 points)

Decide how many solutions each system has and justify with algebra.

\(y=x^{2}+1\) and \(y=1\) (1 point)
\(y=x^{2}+1\) and \(y=0\) (1 point)

Algebra 1 Graphs Solutions Test: questions 6–8

Question 6: Features of an exponential (3 points)

Let \(f(x)=4\cdot 2^{x}\).

Find the y-intercept. (1 point)
Explain why the graph has no x-intercept. (1 point)
Describe the end behavior as \(x\) gets very large and very small. (1 point)

Question 7: Rewrite exponentials (3 points)

(a) Write \(16^{x}\) as a power of 2. (1 point)

(b) An investment grows by a factor of 1.07 each year, so its value is \(1.07^{t}\) times the deposit. Rewrite this with an exponent of \(12t\) and find the monthly growth rate to the nearest hundredth of a percent. (2 points)