
Concept explainers
To Graph and Find:
Use a table of values to graph y=3x2−6x−2 and state the domain and range.

Answer to Problem 26PPS
Domain is all real numbers.
Range = {y∈R:y≥−5} .
R = set of all real numbers
Explanation of Solution
Given Information:
Given equation is :
y=3x2−6x−2
Concept Used :
- Quadratic Functions:
- Quadratic functions are non-linear and are of the form:
f(x)=ax2+bx+c;a≠0
This is the standard form of Quadratic function.
- Shape of the graph of a Quadratic function is called Parabola.
- Parabolas are symmetric about a central line called Axis Of Symmetry.
- The axis of symmetry intersects a parabola only at one point , called the Vertex.
- Parent Function:
y=x2
- Standard Form :
f(x)=ax2+bx+c;a≠0
- Type of Graph:
Parabola
- Axis of Symmetry:
x=−b2a
- y-intercept = c
- Graph:
- If a > 0 ,
- The graph of ax2+bx+c opens upward.
- The lowest point on the graph is the minimum.
- If a< 0 ,
- The graph of ax2+bx+c opens downward.
- The highest point on the graph is the maximum.
- The maximum or the minimum is the vertex.
- The range of the function will be all real numbers greater than or equal to the minimum value , or all real numbers less than or equal to the maximum value.
Calculation:
Make a table of values for :
y=3x2−6x−2
x | y=3x2−6x−2 | (x,y) |
-1 | 7 | (-1,7) |
0 | -2 | (0,-2) |
1 | -5 | (1,-5) |
2 | -2 | (2,-2) |
3 | 7 | (3,7) |
Graph the ordered pairs , and connect them to create a smooth curve .
The parabola extends to infinity.
For the domain, we see x-coordinate values.Since, the graph takes all x values.
So, the domain is all real numbers.
For range, we see y-coordinate values. The range is all the real numbers greater than or equal to the minimum .So, the range is all real numbers greater than or equal to -5 = {y∈R:y≥−5} as the minimum value is -5.
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