f(x)=-4x^{2}-2x+1 For the quadratic function: a) Find the equation

Yasmin

Yasmin

Answered question

2021-10-18

f(x)=4x22x+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

SchulzD

SchulzD

Skilled2021-10-19Added 83 answers

Step 1
The quadratic equation
f(x)=4x22x+1
We have to solve for part (a), (b) and (c).
Step 2
a) We have
f(x)=4x22x+1
We can write
y=4x22x+1
y=4x22x+14+114
(added and subtracted 14)
y=(2x12)2+34
(y34)=(2x12)2
Step 3
Now axis of symmetry can found as by making (2x12)2=0
(2x12)2=0
(2x12)=0
2x=12
x=14
So, the equation axis of symmetry is x=14
Step 4
b) Vertex can be found as by making (2x12)2=0 and (y34)=0
(2x12)=0 and (y34)=0
2x=12 and y34=0
x=14 and y=34
So, the vertex of parabola is (14, 34)
Step 5
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=(2x12)2+34
(2x12)2=34
But square of any number cannot be negative,
So, x intercept will not be there.

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