Identify the vertex, axis of symmetry, and x-intercept(s). Write the quadratic function in standard form.

Question

f(x) = x2 + 3x + 1/4

Write the quadratic function in standard form.

and

Identify the vertex, axis of symmetry, and x-intercept(s). 

Answer 1

Tatyana:

Complete the square.

f(x) = (x+3/2)² -9/4 + 1/4 = (x+3/2)² -8/4 = (x+3/2)² - 2

For y = (x+3/2)²-2

The vertex is at (-3/2, -2)

To find x- intercepts, set y = 0

0 = (x+3/2)² - 2

(x+3/2)² = 2

(x+3/2) = +/- √2

x = -3/2 +/- √2

I'll let you figure out the axis of symmetry