Chapter 2, Problem 9CT

To determine

To calculate: Vertex, Axis of Symmetry, Intervals where the function is increasing and decreasing.

Answer to Problem 9CT

Vertex is $(0.25,2.5)$

Axis of Symmetry is $x=0.25$

Function is increasing on $(0.25,\infty )$

Function is decreasing on $(-\infty ,0.25)$

Explanation of Solution

Given information: $f(x)=8x^2-4x+3$

Graph:

  

Interpretation: As we can see from the graph the parabola is opening up and its vertex is at $(0.25,2.5)$

The Axis of Symmetry is $x=0.25$ because this is the vertical line that divides the parabola in 2 halves.

We can see as the graph has minimum at the vertex and so the function is decreasing on $(-\infty ,0.25)$ and increasing on $(0.25,\infty )$