Question

graph the parabola and give its vertex, axis of symmetry, x-intercepts, and y-intercept.
y = -3x² + 12x - 6
the vertex is (2,6) .
(type an ordered pair.)
the axis of symmetry is x=2 .
(type an equation. use integers or fractions for any numbers in the equation.)
select the correct choice below and fill in any answer boxes within your choice.
a. the x-intercepts are at
x = 2 + √2, 2 - √2 .
(type an exact answer, using radicals as needed. use a comma to separate answers as needed.)
b. there is no x-intercept.
the y-intercept is at y = .
(type an integer or a decimal.)

Explanation:

Step1: Recall y-intercept definition

The y-intercept of a function is the value of \( y \) when \( x = 0 \). So we substitute \( x = 0 \) into the equation \( y=-3x^{2}+12x - 6 \).

Step2: Substitute \( x = 0 \)

Substitute \( x = 0 \) into \( y=-3x^{2}+12x - 6 \):
\( y=-3(0)^{2}+12(0)-6 \)
Simplify each term: \( -3(0)=0 \), \( 12(0)=0 \), so \( y = 0 + 0-6=-6 \).

Answer:

-6