Part 1: Identify key features and graph a parabola from standard form. Answer the following questions to determine the key features of the parabola based on the
equation shown, and then graph it.
12(x + 3) = (y - 2)^2

a) What is the axis of symmetry of the parabola? Explain how to determine this from the equation.
(1 point)

b) What is the vertex of the parabola? (1 point)

c) What is the focus of the parabola? (2 points)

d) What is the directrix of the parabola? (2 points)

e) Sketch a graph of the parabola and label the vertex, focus, directrix, and axis of symmetry. (4 point

a) The axis of symmetry is the line, y = 2

b)  The vertex  of a parabola is (-3, 2)

c) The focus of the parabola is (0, 2)

d) The directrix of a parabola is, x = -6

e) Please find attached the graph of the parabola

Step-by-step explanation:

a) The function for the parabola can be expressed as follows;

12·(x + 3) = (y - 2)²

The general form of the equation of the parabola is x = a·(y - k)² + h

The axis of symmetry is the line, y = k

By comparison, with the given equation of the parabola, we have;

12·(x + 3) = (y - 2)²

x = (1/12)·(y - 2)² - 3

Therefore;

a = (1/12), k = 2, h = -3

The axis of symmetry is y = k

∴ The axis of symmetry is the line, y = 2

b) The vertex  of a parabola = (h, k)

∴ The vertex  of a parabola = (-3, 2)

c) The focus of a parabola is

Therefore, the focus of the parabola is = (0, 2)

The focus of the parabola = (0, 2)

d) The directrix of a parabola is

The directrix of a parabola is, x = -6

e) Please find attached the graph of the parabola, showing the vertex, focus, directrix, and axis of symmetry, created with Microsoft Excel

x² + 3x + 7 = 0       [ax² + bx + c]

a = 1

b = 3

c = 7

quadratic formula:

    (+/- is this ±)

plug in the numbers into the variables

your answer is a

d. 145*2 is 290 than the total angle is 360 then minus 290 then divide by two