Given The Function F ( X ) = 2 X 2 − 8 X + 8 F(x)=2x^2-8x+8 F ( X ) = 2 X 2 − 8 X + 8 , Calculate The Following Values: F ( − 2 ) = □ F(-2) = \square F ( − 2 ) = □ F ( − 1 ) = □ F(-1) = \square F ( − 1 ) = □ F ( 0 ) = □ F(0) = \square F ( 0 ) = □ F ( 1 ) = □ F(1) = \square F ( 1 ) = □ F ( 2 ) = □ F(2) = \square F ( 2 ) = □

Evaluating the Function $f(x)=2x^2-8x+8$ at Different Values of $x$

In this article, we will be evaluating the function $f(x)=2x^2-8x+8$ at different values of $x$. This involves substituting the given values of $x$ into the function and simplifying the resulting expression to obtain the corresponding value of $f(x)$. We will be evaluating the function at $x=-2$, $x=-1$, $x=0$, $x=1$, and $x=2$.

Evaluating $f(-2)$

To evaluate $f(-2)$, we substitute $x=-2$ into the function $f(x)=2x^2-8x+8$. This gives us:

$f(-2) = 2(-2)^2 - 8(-2) + 8$

We can simplify this expression by first evaluating the exponent:

$(-2)^2 = 4$

Now, we can substitute this value back into the expression:

$f(-2) = 2(4) - 8(-2) + 8$

Next, we can simplify the expression by multiplying the numbers:

$f(-2) = 8 + 16 + 8$

Finally, we can add the numbers to obtain the value of $f(-2)$:

$f(-2) = 32$

Evaluating $f(-1)$

To evaluate $f(-1)$, we substitute $x=-1$ into the function $f(x)=2x^2-8x+8$. This gives us:

$f(-1) = 2(-1)^2 - 8(-1) + 8$

We can simplify this expression by first evaluating the exponent:

$(-1)^2 = 1$

Now, we can substitute this value back into the expression:

$f(-1) = 2(1) - 8(-1) + 8$

Next, we can simplify the expression by multiplying the numbers:

$f(-1) = 2 + 8 + 8$

Finally, we can add the numbers to obtain the value of $f(-1)$:

$f(-1) = 18$

Evaluating $f(0)$

To evaluate $f(0)$, we substitute $x=0$ into the function $f(x)=2x^2-8x+8$. This gives us:

$f(0) = 2(0)^2 - 8(0) + 8$

We can simplify this expression by first evaluating the exponent:

$(0)^2 = 0$

Now, we can substitute this value back into the expression:

$f(0) = 2(0) - 8(0) + 8$

Next, we can simplify the expression by multiplying the numbers:

$f(0) = 0 + 0 + 8$

Finally, we can add the numbers to obtain the value of $f(0)$:

$f(0) = 8$

Evaluating $f(1)$

To evaluate $f(1)$, we substitute $x=1$ into the function $f(x)=2x^2-8x+8$. This gives us:

$f(1) = 2(1)^2 - 8(1) + 8$

We can simplify this expression by first evaluating the exponent:

$(1)^2 = 1$

Now, we can substitute this value back into the expression:

$f(1) = 2(1) - 8(1) + 8$

Next, we can simplify the expression by multiplying the numbers:

$f(1) = 2 - 8 + 8$

Finally, we can add the numbers to obtain the value of $f(1)$:

$f(1) = 2$

Evaluating $f(2)$

To evaluate $f(2)$, we substitute $x=2$ into the function $f(x)=2x^2-8x+8$. This gives us:

$f(2) = 2(2)^2 - 8(2) + 8$

We can simplify this expression by first evaluating the exponent:

$(2)^2 = 4$

Now, we can substitute this value back into the expression:

$f(2) = 2(4) - 8(2) + 8$

Next, we can simplify the expression by multiplying the numbers:

$f(2) = 8 - 16 + 8$

Finally, we can add the numbers to obtain the value of $f(2)$:

$f(2) = 0$

In this article, we evaluated the function $f(x)=2x^2-8x+8$ at different values of $x$. We found that $f(-2)=32$, $f(-1)=18$, $f(0)=8$, $f(1)=2$, and $f(2)=0$. These values can be used to understand the behavior of the function at different points.
Evaluating the Function $f(x)=2x^2-8x+8$ at Different Values of $x$: Q&A

In our previous article, we evaluated the function $f(x)=2x^2-8x+8$ at different values of $x$. We found that $f(-2)=32$, $f(-1)=18$, $f(0)=8$, $f(1)=2$, and $f(2)=0$. In this article, we will answer some frequently asked questions about the function and its evaluation.

Q: What is the purpose of evaluating the function at different values of $x$?

A: Evaluating the function at different values of $x$ helps us understand the behavior of the function at those points. It also helps us to identify any patterns or trends in the function's behavior.

Q: How do I evaluate the function at a given value of $x$?

A: To evaluate the function at a given value of $x$, you simply substitute the value of $x$ into the function and simplify the resulting expression.

Q: What if I get a negative value when evaluating the function?

A: If you get a negative value when evaluating the function, it simply means that the function takes on a negative value at that point. This is a normal and expected result.

Q: Can I use the values of the function at different points to make predictions about the function's behavior?

A: Yes, you can use the values of the function at different points to make predictions about the function's behavior. For example, if you notice that the function takes on a negative value at a certain point, you can predict that the function will take on a negative value at other points in the vicinity.

Q: How do I know if the function is increasing or decreasing at a given point?

A: To determine if the function is increasing or decreasing at a given point, you can evaluate the function at two points on either side of the point in question. If the function takes on a larger value at the point to the right of the point in question, then the function is increasing at that point. If the function takes on a smaller value at the point to the right of the point in question, then the function is decreasing at that point.

Q: Can I use the values of the function at different points to find the maximum or minimum value of the function?

A: Yes, you can use the values of the function at different points to find the maximum or minimum value of the function. For example, if you notice that the function takes on a maximum value at a certain point, you can predict that the function will take on a maximum value at other points in the vicinity.

Q: How do I know if the function is a quadratic function or not?

A: A quadratic function is a function of the form $f(x)=ax^2+bx+c$, where $a$, $b$, and $c$ are constants. If the function you are evaluating is of this form, then it is a quadratic function.

Q: Can I use the values of the function at different points to find the equation of the function?

A: Yes, you can use the values of the function at different points to find the equation of the function. For example, if you know the values of the function at three points, you can use these values to find the equation of the function.

In this article, we answered some frequently asked questions about the function $f(x)=2x^2-8x+8$ and its evaluation. We hope that this article has been helpful in understanding the behavior of the function and how to evaluate it at different values of $x$.