Answer:
- (i) -2, (ii) Attached, (iii) x = - 1, (iv) y=6 maximum, y= - 2 minimum, (v) x = 0.723, (vi) y = - 3, (vii) y = - 1
Explanation:
Given
- Function y = (x + 1)² - 3
(i) Find the value of y when x = - 2
- y = (- 2 + 1)² - 3 = (-1)² - 3 = 1 - 3 = - 2
(ii) See the graph attached
(iii) The axis of symmetry is the vertical line passing through the vertex, which is x + 1 = 0 or x = - 1.
This is also reflected on the attached graph.
(iv) From the graph it is visible that in the given interval the function is decreasing, so the value at x = - 4 is the maximum and the value at x = - 2 is minimum:
- y(-4) = (-4 + 1)² - 3 = 9 - 3 = 6 maximum
- y(-2) = (-2 + 1)² - 3 = 1 - 3 = - 2 minimum
These two points too are given on the same graph.
(v) There ate two x-intercepts, the one on the right is the larger one.
It is (0.732, 0), marked on the graph.
(vi) This function is the standard form of the given:
- (x + 1)² - 3 =
- x² + 2x + 1 - 3 =
- x² + 2x - 2
With the positive leading coefficient of 1, it has a minimum value but no maximum. The minimum of this function is at its vertex, which is (- 1, 3) as per graph.
(vii) The function y = x² + 2x is the translation of the given function up by two units.
So its minimum value is 2 units greater: