Graphs as Solution Sets, Linear-Quadratic Systems and Exponential Expressions: Algebra 1 Math Worksheet – PDF Download

Algebra 1 Graphs Solutions Worksheet: problems 1–5

Problem 1: Is the point a solution?

Decide whether each ordered pair is a solution of \(y=2x-1\). (a) \((3,5)\) (b) \((1,2)\)

Problem 2: Points on a parabola

The graph of \(y=x^{2}+3\) is a curve. Decide whether \((-2,7)\) and \((3,10)\) are on it.

Problem 3: Find the missing coordinate

Each point is on the graph of \(y=x^{2}-6\). Find \(k\) in \((4,k)\), and find both values of \(m\) in \((m,3)\).

Problem 4: Intercepts as solutions

Find the x-intercept and the y-intercept of the graph of \(y=2x-6\) by finding the solutions with \(y=0\) and \(x=0\).

Problem 5: Points and a graph

The line is the graph of \(y=-x+4\). Which of the points A through E are solutions? Check each by substituting.

Algebra 1 Graphs Solutions Worksheet: problems 6–10

Problem 6: Line and parabola: y = x² and y = x + 6

Solve the system \(y=x^{2}\) and \(y=x+6\) algebraically.

Problem 7: System with a trinomial

Solve the system \(y=x^{2}+2x-3\) and \(y=x+3\).

Problem 8: Read and verify

The graph shows \(y=x^{2}-2x-3\) and \(y=x-3\). Estimate the intersection points from the graph, then verify them algebraically.

Problem 9: How many solutions?

The graph shows the parabola \(y=x^{2}-4\) and three horizontal lines. For each line, find how many solutions the system has, and find them when they exist: (a) \(y=5\) (b) \(y=-4\) (c) \(y=-6\).

Problem 10: A line that touches the parabola

Solve the system \(y=x^{2}+2\) and \(y=2x+1\), and tell how many solutions it has.

Algebra 1 Graphs Solutions Worksheet: problems 11–15

Problem 11: Rearranging before factoring

Solve the system \(y=x^{2}-3x\) and \(y=2x-6\).

Problem 12: Downward parabola

Solve the system \(y=-x^{2}+4\) and \(y=-x+2\).

Problem 13: Table for a growth function

Complete a table of values for \(g(x)=4^{x}\) using \(x=-2,-1,0,1,2,3\). Then name the point where the graph crosses the y-axis and the horizontal line the graph approaches as \(x\) decreases.

Problem 14: Features of a growth function

For \(y=5\cdot 3^{x}\), find the intercepts and describe the end behavior as \(x\) gets very large and very small.

Problem 15: Exponential decay

The graph shows \(y=64(\frac{1}{2})^{x}\). State the y-intercept and the end behavior, and find \(y\) when \(x=5\).

Algebra 1 Graphs Solutions Worksheet: problems 16–20

Problem 16: A shifted exponential

The graph shows \(y=2^{x}-4\). Find both intercepts and the horizontal asymptote.

Problem 17: Rewrite with base 2

Rewrite each expression as a power of 2: (a) \(8^{x}\) (b) \(4^{3x}\) (c) \(16^{x/2}\).

Problem 18: A two-year factor

A bee colony has \(P(t)=500(1.2)^{t}\) bees after \(t\) weeks. Rewrite it as a function of \(\frac{t}{2}\), so that the base is the growth factor for 2 weeks, and check with \(t=2\).

Problem 19: Ball on a hill

Diego kicks a ball from the bottom of a hill. Its path is \(y=-x^{2}+6x\) and the hillside is \(y=x\), with \(x\) and \(y\) in feet. Find where the ball lands on the hill.

Problem 20: Savings account, monthly rate

Sofia’s savings account value is \(A=1.06^{t}\) times her deposit after \(t\) years. Rewrite the growth factor as a monthly factor using \(1.06^{t}=(1.06^{1/12})^{12t}\) and give the monthly rate to the nearest hundredth of a percent.

Algebra 1 Graphs Solutions Worksheet: problems 21–23

Problem 21: Growth of 15% per year

The number of subscribers to a school podcast grows 15% each year, so \(N=800(1.15)^{t}\). Rewrite the formula with the months \(12t\) in the exponent and find the monthly growth rate to the nearest hundredth of a percent.

Problem 22: Car value each quarter

The value of Liam’s car is \(V=22000(0.85)^{t}\) dollars after \(t\) years. Rewrite it with the exponent \(4t\) (quarters) and find the percent change per quarter to the nearest tenth of a percent.

Problem 23: Bacteria every 20 minutes

A culture has \(N=100(2)^{t}\) bacteria after \(t\) hours. Rewrite the formula with the exponent \(3t\) (20-minute periods) and find the percent growth every 20 minutes to the nearest percent.

How to use this algebra 1 graphs solutions worksheet

Print this algebra 1 graphs solutions worksheet as a PDF, solve every problem on paper, then compare with the answer key.

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