➕ Algebra 1 · Quadratics
Graphing Quadratic Functions flashcards
Say the answer out loud before you flip. Cards you miss come back sooner; cards you know come back later. That spacing is what builds long-term memory.
All 16 flashcards at a glance
Card 1
What is a quadratic function in standard form?
y = ax2 + bx + c, where a, b and c are numbers and a ≠ 0. Its graph is a parabola.
Card 2
How does the sign of a decide which way a parabola opens?
If a > 0 it opens up, and the vertex is the lowest point. If a < 0 it opens down, and the vertex is the highest point. The signs of b and c do not decide this.
Card 3
Which is narrower, y = 4x2 or y = (1/4)x2?
y = 4x2. A larger |a| makes the parabola narrower.
Card 4
What is the axis of symmetry of y = ax2 + bx + c?
The vertical line x = −b/(2a) (with a ≠ 0). The vertex’s x-coordinate is the same number.
Card 5
Find the vertex of y = x2 + 8x + 9.
x = −8/(2 · 1) = −4. Then y = (−4)2 + 8(−4) + 9 = 16 − 32 + 9 = −7. The vertex is (−4, −7).
Card 6
What is the y-intercept of y = 2x2 − 5x + 9, and where does the graph cross the y-axis?
The y-intercept is c = 9. The graph crosses the y-axis at (0, 9).
Card 7
A parabola has axis x = 6 and passes through (2, 5). What other point with y = 5 is on it?
(10, 5). The x-value 2 is 4 units left of the axis, so go 4 units right of the axis: 6 + 4 = 10.
Card 8
How many x-intercepts can a parabola have?
Two, one or none. For example, y = x2 − 1 has two, y = x2 has one (the point (0, 0)), and y = x2 + 1 has none.
Card 9
What is the minimum value of y = x2 − 14x + 55, and where does it occur?
The axis is x = 14/2 = 7, and y = 49 − 98 + 55 = 6. The minimum value is 6, and it occurs at x = 7.
Card 10
A parabola opens up and has vertex (h, k). What are its domain and range?
Domain: all real numbers (any x can be used, unless a story limits it). Range: all y ≥ k.
Card 11
Why is it easiest to build a table of values around the vertex?
Points that are the same distance from the axis, on opposite sides, have the same y-value. Choose x-values in mirror pairs, calculate one of each pair and copy it.
Card 12
What are the zeros of a quadratic function?
The x-values that make y = 0. They are the x-intercepts, where the graph meets the x-axis at points (p, 0).
Card 13
What is the difference between the vertex and the maximum value?
The vertex is a point (h, k). The maximum value is only its y-value k, and it occurs at x = h (for a parabola that opens down).
Card 14
Why can a not be 0 in y = ax2 + bx + c?
If a = 0 the x2 term disappears and you get y = bx + c, which is a line, not a parabola.
Card 15
Is the vertex of a parabola always its y-intercept point?
No. It is only when b = 0, because then the axis is x = 0 and the vertex is (0, c).
Card 16
In this lesson’s AVOID memory trick, what do the letters stand for?
Axis (x = −b/(2a)), Vertex (substitute to find y), Opens (up or down by the sign of a), Intercepts (the point (0, c), its mirror, and any x-intercepts), Draw a smooth curve.