Pass Check: Quadratic & Non-Linear Graphs
Parabolas: shape, roots, turning point, and reading key features off the curve.
Parabola
The U-shaped or n-shaped curve made by a quadratic graph.
Roots (x-intercepts)
The x-values where the curve crosses the x-axis, where y = 0.
Turning point (vertex)
The minimum or maximum point of the curve.
Line of symmetry
The vertical line through the turning point that splits the curve into two mirror halves.
Quick check
Mixed quiz
1. A parabola has a minimum turning point. What does this tell you about the coefficient of x^2?
2. Does the graph of y=x^2 open upward or downward?
3. For y=-x^2, does the graph open upward or downward?
4. For the reciprocal graph y=1/x, in which quadrants does the graph exist?
5. For the reciprocal graph y=1/x, what happens to y as x gets very large?
6. Find the gradient of the line y = 2x + 1.
7. Find the equation of the line passing through (1, 3) and (4, 9).
8. Find the gradient of the line y = 4x + 2.