(a).

The equation is y = x² + 4x.

Write the equation : y = x² + 4x in complete square form.

To change the expressions (x² + 4x) into a perfect square trinomial add (half the x coefficient)² to each side of the expression.

 Here x coefficient = 4. so, (half the x coefficient)² = (4/2)²= 4.

Add 4 and to each side of the equation.

y + 4 = x² + 4x + 4

y + 4 = (x + 2)²

y = (x + 2)² - 4.

The above equation represent the parabola.

Compare the equation y = (x + 1)² - 4 with standard form of the equation of a parabola with vertex (h, k) and axis of symmetry x = h is y = a(x - h)² + k.

Vertex (h, k ) = (- 2, - 4), and axis of symmetry x = h = - 2.

To find the y - intercept, substitute x = 0 in the y = (x + 1)² - 4.

y = (0 + 2)² - 4

y = 4 - 4

y = 0.

To find the x - intercept, substitute y = 0 in the y = (x + 1)² - 4.

0 = (x + 2)² - 4.

4 = (x + 2)²

± 2 = x + 2

 - 2 ± 2 = x

x = 0 and x = - 4.

Make the table of values to find ordered pairs that satisfy the equation.

Choose values for x and find the corresponding values for y.

1. Draw a coordinate plane.

2. Plot the coordinate points.

3. Connect these points with smooth curve.