Lines and parabolas
The equation of a line from its graph, a parabola’s vertex and intercepts, its equation, and plotting one from vertex form.
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Any spelling of the right answer counts: 0.5 or 1/2, pi/2 or π/2, sine or cosine for the same graph.
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About Lines and parabolas
This unit connects equations to their pictures. A line is set by its slope and its y-intercept. A parabola is set by its vertex and how wide it opens, and the x-intercepts are where it crosses the x-axis.
When you read a graph, find exact points first: where the graph crosses an axis or turns around. Two exact points give you a line, and the vertex plus one more point gives you a parabola.
Keep in mind
- Slope-intercept form: y = mx + b, with slope m and y-intercept b.
- Rise over run: count up or down, then right, between two exact points.
- Vertex form: y = a(x − h)² + k, with the vertex at (h, k).
- If a > 0 the parabola opens up, if a < 0 it opens down.
- The x-intercepts are the solutions of y = 0.
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