f\left(x\right) = - 4\times2 - 2x +1 For the quadratic function: N

akutagawatj

akutagawatj

Answered question

2021-11-19

f(x)=4×22x+1
For the quadratic function:
(a) Find the equation of the axis of symmetry:
(b) Find the vertex:
(c) Find the intercepts and express them as points.

Answer & Explanation

Befory

Befory

Beginner2021-11-20Added 19 answers

(a)
We have
f(x)=4x22x+1
We can write
y=4x22x+1
y=4x22x+14+1+14 (added and subtracted 14 )
y=(2x12)2+34
(y34)=(2x12)2
Now,
Axis of symmetry can be found as by making (2x12)2=0
(2x12)2=0
(2x12)=0
2x=12=0
x=14 So,
The equation of axis of symmetry is x=14
Charles Clute

Charles Clute

Beginner2021-11-21Added 17 answers

(b)
Vertex can be found as by making (2x12)2=0 and (y34)=0
(2x12)=0 and (y34)=
2x=12 and y34=0
x=14 and y=34
So,
The vertex of parabola is (14,34)

Don Sumner

Don Sumner

Skilled2021-11-23Added 184 answers

(c) 
For y intercept; x=0
y=4×022×0+1
y=00+1
y=1
So, y intercept is (0,1)
For x intercept; y=0
0=(2x14)2+34
(2x14)2=34
But square of any number cannot be negative, 
So, x intercept will not be there

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