➕ Algebra 1 · Quadratics
Graphing Quadratic Functions cheat sheet
Everything you need on one page. Print it, or switch on test-yourself mode to blur the answers and check your memory.
Standard form
- y = ax2 + bx + c, with a ≠ 0
- The graph is a parabola
- y-intercept: c, the point (0, c)
Direction and width
- a > 0: opens up (vertex is the lowest point)
- a < 0: opens down (vertex is the highest point)
- Larger |a|: narrower. Smaller |a|: wider.
Graphing steps (AVOID)
- A: Axis of symmetry, x = −b/(2a)
- V: Vertex, substitute that x to find y
- O: Opens up if a > 0, down if a < 0
- I: Intercepts, (0, c), its mirror point, and any x-intercepts
- D: Draw one smooth curve
Mirror points
- Points equally far from the axis, on opposite sides, have the same y-value
- If the axis is x = h, the mirror of x is 2h − x
x-intercepts (zeros)
- Set y = 0 and solve (factor if you can)
- Two, one or none
- With two, the axis is halfway between them
Max, min, domain, range
- Maximum or minimum value is the y-value k of the vertex
- Domain: all real numbers (unless a story limits x)
- Range: y ≥ k (opens up) or y ≤ k (opens down)
Watch out
- Flip the sign of b, then divide by 2a
- Only a decides up or down
- Smooth curve, not a V
Formulas
- Standard form: y = ax2 + bx + c, with a ≠ 0
- Axis of symmetry: x = −b/(2a)
- Vertex: (h, k) with h = −b/(2a) and k = the y-value at x = h
- y-intercept: c (the graph crosses the y-axis at (0, c))
- Mirror point: If the axis is x = h, the points at x and at 2h − x have the same y-value
- x-intercepts: Set y = 0 and solve: two, one or no values
- Range: y ≥ k if a > 0, and y ≤ k if a < 0
Graphing Quadratic Functions cheat sheet from HighSchoolQ.com, for personal study use.