Graphing Quadratic Equations Quiz
Questions: 16 · 10 minutes
1. Where does the graph of y = -2(x + 1)^2 + 8 cross the y-axis?
At (0, 8), obtained by ignoring the squared term
At (0, 6), obtained by substituting x = 0
At (0, -6), obtained by reversing the calculated sign
At (0, 10), obtained by adding 2 instead of subtracting it
2. Which quadratic has the narrowest parabola compared with the others?
y = 0.5x^2, with absolute leading coefficient 0.5
y = -x^2, with absolute leading coefficient 1
y = 3x^2, with absolute leading coefficient 3
y = -2x^2, with absolute leading coefficient 2
3. The height of a tossed object is modeled by h(t) = -5(t - 2)^2 + 25, where t is time in seconds and h is height in meters. What maximum height does the model predict, and when?
A maximum of 20 meters at 2 seconds
A maximum of 2 meters at 25 seconds
A maximum of 25 meters at 5 seconds
A maximum of 25 meters at 2 seconds
4. At which points does y = 2x^2 - 8x + 6 cross the x-axis?
At (1, 0) and (3, 0), from the factors (x - 1)(x - 3)
At (-1, 0) and (-3, 0), using reversed root signs
At (2, 0) and (6, 0), using coefficients as roots
At (0, 1) and (0, 3), placing the roots on the y-axis
5. A parabola has the same shape as y = x^2, opens upward, and has vertex (0, -3). Which equation matches its graph?
y = (x - 3)^2, a horizontal shift right by 3
y = x^2 + 3, a vertical shift up by 3
y = x^2 - 3, a vertical shift down by 3
y = -x^2 - 3, a downward-opening parabola shifted down
6. A table lists x-values -2, -1, 0, 1, 2 and corresponding y-values 4, 1, 0, 1, 4. Which equation matches the table?
y = x^2, producing symmetric square values
y = 2x, producing a linear pattern with negative outputs
y = x^2 + 1, producing a y-value of 1 when x = 0
y = |x|, producing outputs 2, 1, 0, 1, 2
7. For y = ax^2 + bx + c, which formula gives the axis of symmetry?
Divide negative b by a: x = -b/a
Divide negative c by twice a: x = -c/(2a)
Use the discriminant expression: x = b^2 - 4ac
Divide negative b by twice a: x = -b/(2a)
8. A parabola has x-intercepts at x = -1 and x = 5. What is its axis of symmetry?
x = -3, the negative of the intercepts' half-distance
x = 2, the midpoint between the two intercepts
x = 3, half the distance between the intercepts
x = -2, the opposite of the intercepts' midpoint
9. What does the graph of y = x^2 + 2x + 5 do relative to the x-axis?
It has no x-intercepts and remains above the x-axis.
It touches the x-axis once at its vertex.
It crosses the x-axis at two distinct points.
It has no x-intercepts and remains below the x-axis.
10. A parabola has vertex (1, -4) and passes through (3, 4). Which equation represents it?
y = (x - 1)^2 - 4, which uses a vertical factor of 1
y = 2(x - 1)^2 - 4, which uses a vertical factor of 2
y = 2(x + 1)^2 - 4, which places the vertex at x = -1
y = -2(x - 1)^2 + 4, which opens downward from a different vertex
11. A quadratic has zeros at x = 2 and x = -3 and passes through (0, -6). Which equation represents it?
y = x^2 + x - 6, equivalent to (x - 2)(x + 3)
y = x^2 + 5x - 6, which has zeros 1 and -6
y = -x^2 - x + 6, which has the stated zeros but the wrong value at x = 0
y = x^2 - x - 6, equivalent to (x - 3)(x + 2)
12. What is the vertex of y = 2(x - 3)^2 - 5?
The point 3 units left and 5 units down: (-3, -5)
The point 5 units left and 3 units up: (-5, 3)
The point 3 units right and 5 units up: (3, 5)
The point 3 units right and 5 units down: (3, -5)
13. Which sequence of transformations changes y = x^2 into y = -(x + 2)^2 + 3?
Shift right 2, reflect across the x-axis, and shift up 3
Shift left 2, reflect across the y-axis, and shift down 3
Shift left 2, reflect across the x-axis, and shift up 3
Shift right 2, reflect across the y-axis, and shift up 3
14. A student wants to graph y = x^2 - 4x + 3 by locating its vertex first. Which vertex should the student plot?
Plot (-2, -1), using a negative x-coordinate for the symmetry line
Plot (2, 1), placing the turning point above the x-axis
Plot (4, 3), using the linear and constant coefficients directly
Plot (2, -1), where the parabola reaches its minimum
15. Which vertex-form equation is equivalent to y = x^2 + 6x + 5?
y = (x - 3)^2 - 4, corresponding to a rightward shift
y = (x + 3)^2 - 4, obtained by completing the square correctly
y = (x + 3)^2 + 4, using the wrong sign for the vertical term
y = (x + 6)^2 + 5, using the linear coefficient as the horizontal shift
16. What is the range of y = -(x - 4)^2 + 7?
All output values at or above 7: y >= 7
All input values at or below 4: x <= 4
All output values at or below 7: y <= 7
Every real y-value, with no upper or lower bound