Graphing Quadratic Functions: Algebra 1 Math Test – PDF Download

Question 1: Features from standard form (2 points)

Consider \(f(x)=2x^{2}-8x+6\).

1. Does the parabola open up or down? Find the y-intercept. (1 point)
2. Find the axis of symmetry and the vertex. (1 point)

Question 2: Read a graph (2 points)

The graph of a quadratic function is shown.

1. Name the vertex and the axis of symmetry. (1 point)
2. Name the x-intercepts and the y-intercept. (1 point)

Question 3: Factored form (2 points)

The function \(g(x)=(x+1)(x-5)\) is given.

1. Find the x-intercepts and the axis of symmetry. (1 point)
2. Find the vertex. (1 point)

Question 4: Complete the square (3 points)

Rewrite \(h(x)=x^{2}+10x+16\) in vertex form. Give the vertex and the zeros of \(h\).

Question 5: Change the form (2 points)

A function is \(y=-2(x-1)^{2}+8\).

1. Write it in standard form. (1 point)
2. Write it in factored form. (1 point)

Question 6: Compare two functions (2 points)

A function \(q\) is shown in the table, and \(r(x)=x^{2}+2x-5\).

1. Name the vertex and the axis of symmetry of \(q\). (1 point)
2. Which function has the smaller minimum value? (1 point)

Question 7: Kicked ball (3 points)

Jamal kicks a ball. Its height in feet after \(t\) seconds is \(h(t)=-16t^{2}+48t\), as the graph shows.

1. Find the maximum height and the time when it happens. (1 point)
2. After how many seconds does the ball hit the ground? (1 point)
3. Find the height after 1 second. (1 point)

Question 8: Intervals of a function (2 points)

The graph of \(f\) is shown.

1. On which interval is \(f\) decreasing? (1 point)
2. For which values of \(x\) is \(f(x) < 0\)? (1 point)

Question 9: Pen with fence (2 points)

Sofia has 60 feet of fence for a rectangular pen against a barn wall, so only three sides need fence. Each of the two sides that touch the wall has length \(x\).

1. Write the area as a function of \(x\). (1 point)
2. Find the largest possible area. (1 point)

⬇ Download the Algebra 1 Graphing Quadratic Functions test (PDF, 95 KB)

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