Last updated: October 22, 2026 · Written by the Math Made Easy math teachers
These 20 problems train standards A-REI.D.10, A-REI.C.7, F-IF.C.7e and A-SSE.B.3c. The first problems test points against equations and evaluate exponential functions. Later problems solve a line with a parabola, graph exponentials and rewrite exponents.
The last six problems apply these ideas to ramps, savings, half-life and exact intersections.
Standards: A-REI.D.10, A-REI.C.7, F-IF.C.7e, A-SSE.B.3c · Level: Grade 9 Algebra 1
Problem 1 Test Two Points on a Line ★★★
Decide whether each point is on the graph of y = 2x + 5: (3, 11) and (−1, 4).
Problem 2 Test Three Points on a Parabola ★★★
Decide which of the points (4, 10), (−3, 3) and (2, −1) are on the graph of y = x² − 6.
Problem 3 Complete the Solution Pair ★★★
Find the missing coordinate so that each point is on the graph.
- (4, ?) on y = 3x − 7
- (−3, ?) on y = x² + 2x
Problem 4 Growth y-Intercept and a Value ★★★
For y = 5(2)x, give the y-intercept and the value at x = 3. Does the graph rise or fall as x increases?
Problem 5 Decay y-Intercept and a Value ★★★
For y = 80(12)x, give the y-intercept, the value at x = 3 and the horizontal asymptote.
Problem 6 Negative Inputs ★★★
For y = 6(3)x, find y when x = −1 and when x = −2.
Problem 7 Find Intersections from a Graph ★★★
The graph shows y = x² − 4 and y = x − 2. Estimate the intersection points, then confirm them algebraically.
Problem 8 Substitution with y = x² ★★★
Solve the system y = x² and y = 2x + 8.
Problem 9 System with a Missing Constant Term ★★★
Solve the system y = x² − x − 6 and y = 2x − 6.
Problem 10 Exactly One Solution ★★★
Solve the system y = x² − 6x + 10 and y = 2x − 6. What does the number of solutions tell you about the graphs?
Problem 11 No Solution ★★★
Show that the system y = x² + 3 and y = 2x has no real solution.
Problem 12 Tangent Condition ★★★
For what value of c does the line y = 2x + c touch the parabola y = x² at exactly one point? Find that point.
Problem 13 Read an Exponential Graph ★★★
The graph shows an exponential function. Give its y-intercept, its horizontal asymptote and its end behavior as x → ∞ and as x → −∞. Write its equation.
Problem 14 Rewrite with the Power Rule ★★★
Rewrite 100(1.08)t, where t is in years, so that the exponent counts months, n = 12t. Find the monthly growth factor to four decimal places.
Problem 15 Ball Over a Ramp ★★★
A ball follows the path h = −x² + 6x, and a ramp is the line h = x + 4 (both in feet). Find where the ball path meets the ramp.
Problem 16 Solve and Check Both Equations ★★★
Solve y = x² − 2x − 8 and y = −x + 4. Check each solution in both equations.
Problem 17 Monthly Rate for a Savings Account ★★★
An account grows by 6% each year: A = 1500(1.06)t. Rewrite it with an exponent that counts months, find the monthly growth rate (to the nearest hundredth of a percent) and find the balance after 18 months.
Problem 18 Half-Life as Yearly Decay ★★★
A radioactive sample has mass M = 200(12) t5 grams after t years. Rewrite it as 200bt, find the yearly decay rate to the nearest tenth of a percent and find the mass after 10 years.
Problem 19 Intercepts and End Behavior ★★★
The graph shows f(x) = 3(2)x − 6. Find the y-intercept and the x-intercept, name the horizontal asymptote and describe the end behavior as x → ∞ and x → −∞.
Problem 20 Irrational Intersection Points ★★★
Find the intersection points of y = x² and y = 2x + 1. Give exact coordinates for the x-values and decimals to the nearest hundredth.
