Question

graph the parabola and give its vertex, axis of symmetry, x-intercepts, and y-intercept.
y = x² + 7x + 12
the vertex is \\(\left(-\frac{7}{2}, -\frac{1}{4}\
ight)\\).
(type an ordered pair.)
the axis of symmetry is \\(x = -\frac{7}{2}\\).
(type an equation. use integers or fractions for any numbers in the equation.)
select the correct choice below and, if necessary, fill in the answer box to complete your choice.
a. the x-intercept(s) is/are at x = -3, -4.
(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 = \\(\square\\).
(simplify your answer.)

Explanation:

Step1: Recall y-intercept definition

The y-intercept of a function is the value of \( y \) when \( x = 0 \).

Step2: Substitute \( x = 0 \) into the equation

For the equation \( y = x^2 + 7x + 12 \), substitute \( x = 0 \):
\( y = (0)^2 + 7(0) + 12 \)
\( y = 0 + 0 + 12 \)
\( y = 12 \)

Answer:

12