Question

Use a graphing calculator to sketch the graph of the quadratic equation, and then state the domain and range y=2x^2-x+3

Answer 1

Answer:

For the domain since we have a quadratic function then the domain would be all the real numbers:

$D =[x | x \in R]$

And if we want to find the range we can find the vertex:

$v_x = -\frac{b}{2a}= -\frac{-1}{2*2}= \frac{1}{4}$

And now we can find th coordinate of y of the vertex like this:

$f(V_x) = 2(\frac{1}{4})^2 -(1/4) +3 =2.875$

And then the range would be:

$R=[x \geq 2.875]$

Step-by-step explanation:

We have the following function given:

$y = 2x^2 -x +3$

For this case we can plot the function with a calculator and we got the plot in the figure attached.

For the domain since we have a quadratic function then the domain would be all the real numbers:

$D =[x | x \in R]$

And if we want to find the range we can find the vertex:

$v_x = -\frac{b}{2a}= -\frac{-1}{2*2}= \frac{1}{4}$

And now we can find th coordinate of y of the vertex like this:

$f(V_x) = 2(\frac{1}{4})^2 -(1/4) +3 =2.875$

And then the range would be:

$R=[x \geq 2.875]$