➕ Algebra 1 · Quadratics
Graphing Quadratic Functions: true or false
Decide fast, then read the reason. Wrong answers are the best teachers, so every statement explains itself.
All statements and answers
The graph of y = 0x2 + 4x + 1 is a parabola.
✗ False. Here a = 0, so the equation is y = 4x + 1, which is a line. A quadratic function needs a ≠ 0.
The graph of y = −3x2 + 4x opens upward because b = 4 is positive.
✗ False. Only a decides the direction. Here a = −3 is negative, so the parabola opens down.
A parabola has axis of symmetry x = 7 and passes through (3, 11). Then (11, 11) is also on it.
✓ True. The x-value 3 is 4 units left of the axis, so the mirror point is 4 units right of it, at x = 7 + 4 = 11, with the same y-value.
The axis of symmetry of y = x2 − 10x + 3 is x = −5.
✗ False. x = −b/(2a) = −(−10)/2 = 5. The sign of b must be flipped, so the axis is x = 5, not x = −5.
The vertex of y = 3x2 + 12x + 17 is (−2, 5).
✓ True. x = −12/(2 · 3) = −2, and y = 3(4) − 24 + 17 = 12 − 24 + 17 = 5.
Every parabola has exactly two x-intercepts.
✗ False. A parabola can have two, one or none. For example, y = (x − 4)2 touches the x-axis only at (4, 0), and y = x2 + 3 never touches it.
The maximum value of a parabola that opens down is the y-value of its vertex.
✓ True. A parabola that opens down is highest at its vertex, so the y-value there is the largest y-value the function takes.
The graph of y = 5x2 is wider than the graph of y = x2.
✗ False. A larger |a| makes the parabola narrower. |5| is greater than |1|, so y = 5x2 is narrower.
The graph of y = x2 − 6x + 11 crosses the y-axis at (0, 11).
✓ True. At x = 0, y = c = 11, so the graph crosses the y-axis at (0, 11).
For y = x2 − 4 with no story attached, the domain is all y ≥ −4.
✗ False. That describes the range. The domain is the x-values you can use, and every real number works, so the domain is all real numbers.
If a parabola models the height of a tossed ball, only the part of the parabola from the toss to the landing describes the ball’s flight.
✓ True. The formula’s parabola continues beyond the flight, for example to times before the toss, but the story does not.
A parabola that opens upward and has its vertex at (−8, 6) crosses the x-axis twice.
✗ False. The vertex is the lowest point and its y-value, 6, is above the x-axis. Every point is at least 6 high, so the parabola never reaches the x-axis.
If a parabola crosses the x-axis at x = 5 and x = 21, its axis of symmetry is x = 13.
✓ True. The axis is halfway between the two x-intercepts: (5 + 21)/2 = 13.