### All Algebra 1 Resources

## Example Questions

### Example Question #1 : How To Graph A Quadratic Function

Which is the graph of ?

**Possible Answers:**

**Correct answer:**

Think of the graph of :

Constants within the parentheses will shift the parabola to the left and right, while terms outside of the parentheses will shift it vertically.

In our equation, there is a -2 term outside the parentheses. This will shift the graph down by 2 units.

The graph of will look like this:

There is also a constant within the parentheses, –1. This will shift the graph to the right by 1 unit.

Therefore will generate a graph like this:

### Example Question #1 : How To Graph A Quadratic Function

What is the minimum possible value of the expression below?

**Possible Answers:**

The expression has no minimum value.

**Correct answer:**

We can determine the lowest possible value of the expression by finding the -coordinate of the vertex of the parabola graphed from the equation . This is done by rewriting the equation in vertex form.

The vertex of the parabola is the point .

The parabola is concave upward (its quadratic coefficient is positive), so represents the minimum value of . This is our answer.

### Example Question #2 : How To Graph A Quadratic Function

What is the vertex of the function ? Is it a maximum or minimum?

**Possible Answers:**

; maximum

; maximum

; minimum

; minimum

**Correct answer:**

; minimum

The equation of a parabola can be written in vertex form: .

The point in this format is the vertex. If is a postive number the vertex is a minimum, and if is a negative number the vertex is a maximum.

In this example, . The positive value means the vertex is a minimum.

### Example Question #36 : Polynomial Functions

Which of the graphs best represents the following function?

**Possible Answers:**

None of these

**Correct answer:**

The highest exponent of the variable term is two (). This tells that this function is quadratic, meaning that it is a parabola.

The graph below will be the answer, as it shows a parabolic curve.

### Example Question #7 : Parabolic Functions

What is the equation of a parabola with vertex and -intercept ?

**Possible Answers:**

**Correct answer:**

From the vertex, we know that the equation of the parabola will take the form for some .

To calculate that , we plug in the values from the other point we are given, , and solve for :

Now the equation is . This is not an answer choice, so we need to rewrite it in some way.

Expand the squared term:

Distribute the fraction through the parentheses:

Combine like terms:

### Example Question #3 : How To Graph A Quadratic Function

**Possible Answers:**

None of the above

**Correct answer:**

Starting with

moves the parabola by units to the right.

Similarly moves the parabola by units to the left.

Hence the correct answer is option .

### All Algebra 1 Resources

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