Answer:
(a) y-intercept: (0, -9) or y = -9
zeros: (-3, 0) (3, 0) or x = -3, x = 3
Axis of symmetry: x = 0
vertex: (0, -9)
(b) y-intercept: (0, 4) or y = 4
zeros: (2, 0) or x = 2
Axis of symmetry: x = 2
vertex: (2, 0)
(c) y-intercept: (0, 18) or y = 18
zeros: (-3, 0) or x = -3
Axis of symmetry: x = -3
vertex: (-3, 0)
Step-by-step explanation:
(a) [tex]y=(x-3)(x+3)[/tex]
y-intercept: when x = 0
[tex]\implies (0-3)(0+3)=-9[/tex]
zeros: when y = 0
[tex]\implies (x-3)(x+3)=0[/tex]
[tex]\implies(x-3)=0 \implies x=3[/tex]
[tex]\implies (x+3)=0 \implies x=-3[/tex]
Axis of symmetry: midpoint of the zeros
[tex]x=\dfrac{3-(-3)}{2}+(-3)=0[/tex]
Vertex: turning point of the curve, where x is the line of symmetry
[tex]\implies (0-3)(0+3)=-9[/tex]
Therefore: (0, -9)
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(b) [tex]y=(x-2)(x-2)[/tex]
y-intercept: when x = 0
[tex]\implies (0-2)(0-2)=4[/tex]
zeros: when y = 0
[tex]\implies (x-2)(x-2)=0[/tex]
[tex]\implies(x-2)=0 \implies x=2[/tex]
with multiplicity 2
Axis of symmetry:
As there is one zero with multiplicity 2,
the axis of symmetry is x = 2
Vertex: turning point of the curve, where x is the line of symmetry
[tex]\implies (2-2)(2-2)=0[/tex]
Therefore: (2, 0)
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(c) [tex]y=2(x+3)^2[/tex]
y-intercept: when x = 0
[tex]\implies 2(0+3)^2=18[/tex]
zeros: when y = 0
[tex]\implies 2(x+3)^2=0[/tex]
[tex]\implies (x+3)^2=0[/tex]
[tex]\implies (x+3)=0[/tex]
[tex]\implies x=-3[/tex] with multiplicity 2
Axis of symmetry:
As there is one zero with multiplicity 2,
the axis of symmetry is x = -3
Vertex: turning point of the curve, where x is the line of symmetry
[tex]\implies 2(-3+3)^2=0[/tex]
Therefore: (-3, 0)
