Transforming Quadratic Functions in Vertex Form

If a quadratic function is in the form y = a(x-h)^2 + k, what does 'h' represent?

• Rate of change of the parabola

• Vertical shift of the parabola

• Y-intercept of the parabola

• Horizontal shift of the parabola

Explain how to determine the vertex of a quadratic function in vertex form.

• The vertex is always at (0, 0) for all quadratic functions

• The vertex of a quadratic function in vertex form is at the point (h, k) where 'h' and 'k' are the values in the equation y = a(x - h)^2 + k.

• The vertex is determined by finding the x-intercept of the function

• The vertex is located at the highest point of the parabola

In the vertex form f(x) = a(x - h)² + k , what does the 'k' value do?

• Shifts the function left or right

• Reflects over the x-axis

• Vertical stretch or compression

• Shifts the function up or down

Given f(x) = (x + 3)² , how did we transform from the parent function?

• Horizontal shift left 3

• Vertical shift up 3

• Horizontal shift right 3

• Vertical shift down 3

Convert to vertex form:
f(x) = x² + 10x + 24

• f(x) = ( x - 5 )² + 1

• f(x) = ( x + 5 )² - 1

• f(x) = ( x - 5 )² - 1

• f(x) = ( x + 5 )² + 1

Which of the following shows
f(x) = x² + 12x - 2
written in vertex form?

• f(x) = (x + 6)² + 142

• f(x) = (x + 6)² - 34

• f(x) = (x + 6)² - 38

• f(x) = (x + 6)² + 34

Convert to Vertex Form: f(x) = x² +8x +14

• f(x) = (x - 4)² + 2

• f(x) = (x - 4)² - 2

• f(x) = (x + 4)² + 2

• f(x) = (x + 4)² - 2

Which of the following shows
f(x) = x² - 8x + 1
written in vertex form?

• f(x) = (x - 4)² - 15

• f(x) = (x - 4)² + 17

• f(x) = (x - 4)² - 17

• f(x) = (x - 4)² + 65

Change x²-16x+64 to vertex form.

• (x-16)²

• (x+16)²

• (x-8)²

• (x+8)²

What steps transform the graph y = x² to y = 2(x+2)² - 5?

• Compress by 2, shifted 2 units left and 5 down

• Stretch by 5, shifted 5 units left and 2 down

• Stretch by 2, shifted 2 units left and 5 down

• Compress by 5, shifted 2 units left and 2 down