Question

2. Consider the quadratic function range: f(x) = 2x² - 4x + 6

a. Determine the equation of the axis of symmetry
b. Write the equation in vertex form
C. Determine the minimum or maximum value.
d. List the x-intercepts from the graph.
e. List the y-intercept.
f. Graph the function.
g. Domain:
Range:

Answer 1

The equation of the axis of symmetry is x = 1

The equation in vertex form is y = 2(x - 1)² + 4

Minimum = 4

x-intercepts = None

y-intercepts = 6

The domain is the set of all real values, and the range is (4, ∞)

How to determine the properties of the function

From the question, we have the following parameters that can be used in our computation:

y = 2x² - 4x + 6

The equation of the axis of symmetry is

x = -b/2a

So, we have

x = 4/(2 * 2)

x = 1

So, the y coordinate of the vertex is

y = 2(1)² - 4(1) + 6

y = 4

So, the equation in vertex form is

y = 2(x - 1)² + 4

The vertex is the minimum of the function

So, we have

Minimum = 4

From the graph, we have the intercepts to be

x-intercepts = None

y-intercepts = 6

The domain is the set of all real values, and the range is (4, ∞)