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(i) The axis of symmetry is .

(ii) The axis of symmetry is .

(iii) The axis of symmetry is .

Step-by-step explanation:

We proceed to explain how we determine the expression for the axis of symmetry for each case:

(i)

The expression depicts a vertical parabola, meaning that axis of symmetry is vertical, that is, a function of the form . This line passes through the vertex of the parabola. The component contains the information of the horizontal component of the vertex, where the axis passes through. Therefore, the axis of symmetry is .

(ii)

At first we complete the square and factor the perfect square trinomial:

By applying the approach used in (i), we find that the axis of symmetry is .

(iii) First, we locate the vertex of the parabola, which is (1,-3). The first component of the ordered pair contains all the needed information to determine the equation of the axis of symmetry, which is .

region b will make the inequalities y < 2x + 1 and y > -x - 2 true ⇒ answer a

step-by-step explanation:

* lets study the graph and the inequality to solve the question

- the inequality y > -x - 2

∵ the form of the inequality is y > mx + c , m is the slope of the line

  and c is the y-intercept (the line intersect y-axis at point (0 , c)

∴ c = -2 that means the line intersect the y-axis at point (0 , -2)

∵ the sign of the inequality is >

∴ we shad the part over the line

  region a and b

- the inequality y < 2x + 1

∵ the form of the inequality is y > mx + c , m is the slope of the line

  and c is the y-intercept (the line intersect y-axis at point (0 , c)

∴ c = 1 that means the line intersect the y-axis at point (0 , 1)

∵ the sign of the inequality is <

∴ we shad the part under the line

  region b and c

∵ the common region between the two lines is region b

∴ region b will make the inequalities y < 2x + 1 and y > -x - 2 true

hi im bob : l

step-by-step explanation: