Which of the following statements are true about the quadratic function f(x)=a(x-h)^2 +k that has no real zeros? Select all that apply.

Question

Generate a visually appealing image composed of a large and simply stylized quadratic function graph. This graph should be presented as a parabola, opening either upwards or downwards, with no intersections with the x-axis, as per the description of a quadratic function with no real zeros. Please avoid any text in the image.

Which of the following statements are true about the quadratic function f(x)=a(x-h)^2 +k that has no real zeros? Select all that apply.

A- the value of a must be greater than one, so the graph is vertically stretched.
B- the value of h cannot be zero.
C - the values of a and k must have opposite signs.
D- if the value of a is positive, then the value of k is negative.
E- if the value of k is negative , then the value of a is negative.
F- the value of k cannot be zero.
G- if the value of a is positive, then the graph opens upward.

Answer 1

C- the values of a and k must have opposite signs.

D- if the value of a is positive, then the value of k is negative.
F- the value of k cannot be zero.
G- if the value of a is positive, then the graph opens upward.