Question

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.

If the value of k is negative, then the value of a is negative

The value of a must greater than one, so the graph is vertically stretched.

If the value of a is positive, then the value of k is negative

The values of a and k must have opposite signs

The value of k cannot be 0

If the value of a is positive, then the graph opens upward.

The value of h cannot be zero

Answer 1

If f(x)=a(x-h)^2+k has no real zeros then
a > 0, k > 0
or
a < 0 and k < 0

Answer 2

If the value of k is negative, then the value of a is negative

The value of a must greater than one, so the graph is vertically stretched.

The value of k cannot be 0

If the value of a is positive, then the graph opens upward.

Answer 3

That is correct. If the quadratic function f(x) = a(x-h)^2 + k has no real zeros, it means the vertex of the parabola is above the x-axis (if a > 0) or below the x-axis (if a < 0). This implies that k is greater than 0 when a is greater than 0, and k is less than 0 when a is less than 0. So, a > 0 and k > 0 or a < 0 and k < 0.