Janelle S. answered • 02/08/21

Penn State Grad for ME, Math & Test Prep Tutoring (10+ yrs experience)

vertex = (h,k) = (2,-3)

vertex form of equation: y = a(x - h)^{2} + k = a(x - 2)^{2} - 3

Based on the vertex, you know that the parabola will have a minimum or maximum at the point (2,-3). If the x^{2} term is positive, the parabola will extend upwards and cross the x-axis, creating x-intercepts. If the x^{2} term is negative, the parabola will extend downwards and not cross the x-axis. Set a as any negative number so that the parabola doesn't have any x-intercepts.

y = -(x - 2)^{2} - 3 = -x^{2} + 4x - 4 - 3 = -x^{2} + 4x - 7

Summer E.

Thank you, this helps me alot. At first I was confused but the negitive number makes it so no x-intercepts.02/08/21