Question

learning goals from lesson 3.3
✓ i can graph quadratic functions of the form ( f(x)=a x^{2}+) ( b x+c ) and find maximum and minimum values of quadratic functions. (standards: a.ced.2, f.if.4, f.if.5, f.if.7a, f.if.9)
lesson reflection (circle one)
i got it! im still learning it.

1. find the axis of symmetry and the vertex of the graph of ( f(x)=3 x^{2}-6 x - 1 ).

a. the axis of symmetry is ( x = 1 ).
the vertex is ( (1,-4) ).
b. the axis of symmetry is ( x=-1 ).
the vertex is ( (-1,-1) ).
c. the axis of symmetry is ( x = 1 ).
the vertex is ( (1,8) ).
d. the axis of symmetry is ( x=-1 ).
the vertex is ( (-1,8) ).

Explanation:

Step1: Find the axis of symmetry

For a quadratic function \(y = ax^{2}+bx + c\), the formula for the axis of symmetry is \(x=-\frac{b}{2a}\).
Given \(f(x)=3x^{2}-6x - 1\), where \(a = 3\) and \(b=-6\).
Substitute \(a\) and \(b\) into the formula: \(x =-\frac{-6}{2\times3}=1\).

Step2: Find the vertex

The vertex lies on the axis of symmetry. So we substitute \(x = 1\) into the function \(f(x)=3x^{2}-6x - 1\).
\(f(1)=3\times(1)^{2}-6\times(1)-1=3 - 6-1=-4\).

Answer:

A. The axis of symmetry is \(x = 1\). The vertex is \((1,-4)\)