Reading and forming parabolas in vertex form y = a(x - h)^2 + k where a is not 1

Task goals

• Read the vertex, axis of symmetry, opening direction, and width (narrower/wider than y=x^2) directly from an equation in vertex form y=a(x-h)^2+k.
• Substitute values of x into y=a(x-h)^2+k to find corresponding y-values, including the y-intercept at x=0.
• Find two extra symmetric points either side of the axis of symmetry.
• Solve a(x-h)^2+k=0 to find the x-intercepts, or explain why none exist.
• Given a vertex and one other point on the parabola, write the equation in vertex form, including solving for an unknown a.
• Given a vertex and both roots (x-intercepts), write the equation in vertex form.
• Compare or reason about how changing a affects the width, opening direction, or steepness of a parabola without changing its vertex.