Determine the vertex and axis of symmetry of the following

William Curry

William Curry

Answered question

2021-12-11

Determine the vertex and axis of symmetry of the following quadratics.
a) f(x)=2(x3)21
b) f(x)=x2+4x+3

Answer & Explanation

Esta Hurtado

Esta Hurtado

Beginner2021-12-12Added 39 answers

Step 1
For a quadratic equation y=ax2+bx+c
Axis of Symmetry is x=b2a
x-coordinate of vertex is b2a
a) f(x)=2(x3)21
=2(x26x+9)1
f(x)=2x212x+17
Axis of symmetry x=b2a
x=(12)2(2)=3
x=3
Step 2
x-coordinate of vertex =b2a=3
y-coordinate of vertex =f(b2a)=f(3)
=2(33)21=1
Vertex =(3, 1)
b) f(x)=x2+4x+3
Axis of symmetry
x=b2a=42(1)=2
x=2
x-coordinate of vertex =b2a=2
Step 3
y-coordinate of vertex
=f(b2a)
=f(2)
=(2)2+4(2)+3
=1
Vertex =(2, 1)
Donald Cheek

Donald Cheek

Beginner2021-12-13Added 41 answers

Step 1
f(x)=2(x3)21
Multiply 2 and 2 to get 4.
4(x3)1
Use the distributive property to multiply 4 by x3.
4x121
Subtract 1 from -12 to get -13
4x13
Step 2
f(x)=x2+4x+3
Factor the expression by grouping. First, the expression needs to be rewritten as x2+ax+bx+3. To find a and b, set up a system to be solved
a+b=4
ab=1×3=3
Since ab is positive, a and b have the same sign. Since a+b is positive, a and b are both positive. The only such pair is the system solution.
a=1
b=3
Rewrite x2+4x+3 as (x2+x)+(3x+3)
(x2+x)+(3x+3)
Factor out x in the first and 3 in the second group.
x(x+1)+3(x+1)
Factor out common term x+1 by using distributive property.
(x+1)(x+3)

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