Exploring Vertex Form of Quadratic Functions

What is the vertex form of a quadratic function?

• y = ax^2 + bx + c

• y = a(x - h)^2 + k

• y = a(x + h)^2 + k

• y = a(x - h)^2 - k

In the vertex form y = a(x - h)^2 + k, what do h and k represent?

• The roots of the equation

• The axis of symmetry

• The vertex of the parabola

• The coefficients of x

What effect does a negative sign in front of the quadratic term have on the graph?

• It reflects the graph over the x-axis

• It shifts the graph upward

• It makes the graph narrower

• It shifts the graph to the right

What is the correct terminology for making a parabola wider?

• Horizontal stretch

• Vertical stretch

• Vertical shrink

• Horizontal shrink

If a quadratic function has a vertex at (3, 4) and opens upwards, what is the minimum value?

• 3

• 4

• 0

• Infinity

What is the axis of symmetry for the quadratic function f(x) = 2(x - 3)^2 + 4?

• x = 2

• x = -3

• x = 3

• x = 4

What is the domain of any quadratic function?

• Depends on the function

• Negative infinity to 0

• 0 to positive infinity

• Negative infinity to positive infinity

Given the vertex (1, 20) and a point (0, 4) on the parabola, what is the value of 'a' in the vertex form equation?

• 16

• 1

• -16

• -1

What is the vertex form of the quadratic function with vertex (1, 20) and 'a' value of -16?

• y = -16(x + 1)^2 + 20

• y = -16(x - 1)^2 + 20

• y = 16(x - 1)^2 + 20

• y = -16(x - 1)^2 - 20

What is the standard form of the quadratic function y = -16(x - 1)^2 + 20?

• y = -16x^2 + 32x + 4

• y = -16x^2 + 32x - 4

• y = -16x^2 - 32x + 4

• y = 16x^2 - 32x + 4