💥 Q16 : Prep 3 Algebra Question Bank T1

a. Represent the function graphically and deduce deduce the coordinates of the vertex of the curve a the equation of the line of symmetry and the maximum or minimum value of the function: \[ f(x) = x(x - 2) - 3 \, \text{where} \, x \in [-2, 4] \]

(a) Vertex: (2, -3), Symmetry: x=2, Min: -3

(b) Vertex: (0, -3), Symmetry: x=0, Min: -3

(c) Vertex: (1, -4), Symmetry: x=1, Min: -4

(d) Vertex: (-1, 0), Symmetry: x=-1, Min: 0

From the graph we find:
• The vertex of the curve is \((1, -4)\)
• The equation of the line of symmetry is \(x = 1\)
• The minimum value \(= -4\)

MR/Nasef.N

b. Represent the function graphically and deduce deduce the coordinates of the vertex of the curve a the equation of the line of symmetry and the maximum or minimum value of the function: \[ f(x) = 3 - 2x - x^2 \, \text{where} \, x \in [-4, 2] \]

(a) Vertex: (1, 0), Symmetry: x=1, Max: 0

(b) Vertex: (-2, 3), Symmetry: x=-2, Max: 3

(c) Vertex: (-1, 4), Symmetry: x=-1, Max: 4

(d) Vertex: (0, 3), Symmetry: x=0, Max: 3

From the graph we find:
• The vertex of the curve is \((-1, 4)\)
• The equation of the line of symmetry is \(x = -1\)
• The maximum value \(= 4\)

MR/Nasef.N

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