What is the equation for parabola that has the vertex of (2,-3) but has NO x intercepts

Question

It does have y-intercepts.

Answer 1

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 x² term is positive, the parabola will extend upwards and cross the x-axis, creating x-intercepts. If the x² 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 = -x² + 4x - 4 - 3 = -x² + 4x - 7