Graphs and Solutions Test – Algebra 1 Math (Printable PDF)

Question 1 Points on a Parabola (2 points)

Which of the points (2, −3), (−1, 2) and (4, 5) lie on the graph of y = x² − 2x − 3? Show your work.

Question 2 Line and Parabola (3 points)

Solve the system y = x² − 4x + 3 and y = x − 1.

1. Write the equation you get by setting the expressions equal. (1 point)
2. Solve it for x. (1 point)
3. Find the matching y-values. (1 point)

Question 3 Estimate Then Confirm (3 points)

The graph shows a parabola (solid) and a line (dashed).

1. Estimate the intersection points from the graph. (1 point)
2. The curves are y = x² − 2x − 3 and y = x − 3. Confirm your estimate algebraically. (2 points)

Question 4 No Intersection (2 points)

Show that the line y = 2x − 3 and the parabola y = x² + 1 do not intersect.

Question 5 Exponential Graph (3 points)

The graph shows an exponential function.

1. Give the y-intercept and write the equation. (1 point)
2. Describe the end behavior as x → ∞ and x → −∞. (1 point)
3. Find the value of the function at x = −5. (1 point)

Question 6 Monthly Growth Factor (3 points)

A balance is modeled by A = 800(1.12)^t, where t is in years.

1. Rewrite A with an exponent equal to the number of months and give the monthly factor to four decimal places. (2 points)
2. Find the balance after 6 months, to the nearest cent. (1 point)

Question 7 System Solution Check (2 points)

Show that (3, 9) is a solution of the system y = x² and y = 4x − 3, then find the other solution.

Question 8 Rewrite an Exponent (2 points)

Rewrite 5^{x + 2} in the form a · 5^x, then evaluate it at x = 1.