Calculating Axis of Symmetry, Vertex and Y Intercept

Convert the equation y= x²-2x-5 into vertex form. 

• y= (x-1)²-6

• y= -(x-1)²-6

• y= (x+1)²-6

• y= -(x+6)²-1

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

Which of the following is the correct equation for the given graph? (Hint: use the axis of symmetry and y intercept or vertex for each answer choice to match to the graph)

• f(x) = x² - 4x - 3

• f(x) = x² + 4x + 3

• f(x) = x² - 4x + 3

• f(x) = x² + 4x - 3

Explain how to find the vertex of a parabola given a quadratic function in standard form.

• The vertex can be found by taking the square root of the discriminant

• The vertex of the parabola can be found by calculating x = -b / (2a) and then substituting this x-value back into the original function to find the y-coordinate.

• The vertex is located at the y-intercept of the parabola

• The vertex is always at (0,0) for any parabola

Explain how to determine the axis of symmetry of a parabola given a quadratic function in standard form.

• Calculate x = -b / (2a) to find the axis of symmetry

• The axis of symmetry is always at x = 0 for any parabola

• Look at the y-intercept to determine the axis of symmetry

• Check the discriminant to find the axis of symmetry

What is the vertex form of a quadratic function?

• y = a(x - h)^2 - k

• y = a(x + h)^2 + k

• y = a(x + h)^2 - k

• y = a(x - h)^2 + k

The cross-section of a parabolic reflector has a vertical axis of symmetry with its vertex at (0,0). The focus of the reflector is 4 feet above the vertex. The reflector extends 5 feet to either side of the vertex. What is the depth of the reflector? Round your answer to the nearest hundredth.

The depth of the reflector is about (a)   feet.