Solving contextual problems with parabolas (a=1)

Task goals

• Read the vertex, axis of symmetry, x-intercepts, and y-intercept of a parabola given in vertex form, for both upward-opening (minimum) and downward-opening (maximum) graphs.
• Interpret what the vertex, an x-intercept, or the y-intercept means in a real-world context, such as a ball's maximum height, when a projectile lands, or when a profit is zero.
• Use the axis of symmetry to find a second point on the parabola that mirrors a known point, without needing to solve or expand the equation.
• Find the interval of x-values for which a parabola's y-values are above, below, at least, or at most a given value.
• Estimate a parabola's x-intercepts to one decimal place when they are not integers.
• Explain why a parabola has no real x-intercepts, or determine without expanding whether a given point lies on the graph.
• Compare the width of two parabolas with different leading coefficients and explain how the leading coefficient changes the graph's shape.