Quadratic Functions Test – Algebra 1 Math (Printable PDF)

Question 1 Vertex Form Features (2 points)

Consider y = −3(x + 2)² + 7.

1. Name the turning point and the direction of opening. (1 point)
2. Give the mirror line and the extreme value of y. (1 point)

Question 2 Vertex from Standard Form (2 points)

For y = x² − 10x + 7, find the mirror line, the turning point and the point where the graph meets the y-axis.

Question 3 Complete the Square (2 points)

Complete the square to rewrite y = x² + 12x + 31, then name the turning point.

Question 4 Features from a Graph (3 points)

Study the parabola drawn below.

1. Name its turning point and its mirror line. (1 point)
2. Name every point where it meets an axis. (1 point)
3. State the domain and the range. (1 point)

Question 5 Factored Form (2 points)

Without expanding, find where y = (x + 3)(x − 7) meets the x-axis and where it turns.

Question 6 Write an Equation (3 points)

A parabola turns at (3, 1) and contains the point (5, 9).

1. Find its equation as y = a(x − h)² + k. (2 points)
2. Expand it into standard form. (1 point)

Question 7 Thrown Ball (3 points)

A kicked soccer ball has height h(t) = −16t² + 32t + 48 feet at t seconds, as graphed.

1. How high is the ball at the moment of the kick? (1 point)
2. When is it highest, and how high is it then? (1 point)
3. When does it reach the ground? (1 point)

Question 8 Fenced Pen (2 points)

A horse corral uses 60 feet of rail on all four sides. If the width is w, the length is 30 − w.

1. Write a rule for the area A(w). (1 point)
2. Find the largest possible area and the dimensions that produce it. (1 point)

Question 9 Does It Cross the Axis? (1 point)

Without graphing, decide whether the curve y = 2(x − 1)² + 3 ever touches the x-axis. Justify your answer.