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Answers
Answer:
13) ( d)
14) ( d)
15) ( c)
16) ( c)
Step-by-step explanation:
13)
The adjacent graph cuts the x-axis at (-4,0) .
It is a parabola.
So the roots are -4 and -4
So, The function must be f(x) = (x+4)²
Since,
f(x) = (x+4)²
=> (x+4)² = 0
=> (x+4)(x+4) = 0
=> x+4 = 0 or x+4 = 0
=> x = -4 or x = -4
14)
Given that f(x) = (x-2)²-4
The vertex form of the equation of a parabola that is a function of x is: y=f(x)=a(x−h)²+k
where (h,k) is the vertex.
On comparing this with a(x−h)²+k
a = 1
h = 2
k = -4
(h,k) = (2,-4)
The vertex = (2,-4)
15)
Given that f(x) = (x-2)²-4
=> y = (x-2)²-4
To get x intercept then put y = 0
=> 0 = (x-2)²-4
=> (x-2)² = 4
=> x-2 = ±√4
=> x-2 = ±2
=> x = 2±2
=> x = 2+2 or 2-2
=> x = 4 and 0
=> (x,y) = (4,0) and (0,0)
16)
The adjacent graph cuts the x-axis at (2,0) .
It is a parabola.
So the roots are 2 and 2
So, The function must be f(x) = (x-2)²
Since,
f(x) = (x-2)²
=> (x-2)² = 0
=> (x-2)(x-2) = 0
=> x-2 = 0 or x-2 = 0
=> x = 2 or x = 2