# Algebra II : Quadratic Formula

## Example Questions

### Example Question #141 : Functions And Lines

Which of the following is the correct solution when    is solved using the quadratic equation?

Explanation:

### Example Question #21 : Quadratic Formula

Solve the equation using the quadratic formula.

Explanation:

.

Setting , ,  yields,

### Example Question #21 : Quadratic Formula

Find the roots of:

Since the quadratic cannot be factored, there are no roots.

Explanation:

Identify the values of , and  in the standard form of the parabola.

Calculate the discriminant.

Since the discriminant is less than zero, the quadratic is irreducible and there are no real roots. However, there are complex roots.  Use the quadratic formula to determine the complex roots.

### Example Question #24 : Quadratic Formula

Use the quadratic formula to find the roots of .

and

and

and

no solution

and

Explanation:

The parent function of a quadratic is represented as . The quadratic formula is . In this case , and . Replacing these values into the quadratic forumula will give you the solutions to the quadratic.

and

### Example Question #491 : Intermediate Single Variable Algebra

Explanation:

You must know the quadratic equation .

To plug in the right terms, recognize that polynomials in standard form are symbolized as .

Plug in the values from your equation

Reduce:

Note that this represents two values since there is a  in the equation. One is solved with an addition sign and the other is solved with a subtraction sign to yield two answers or roots where this equation crosses the x axis.

### Example Question #82 : Systems Of Equations

Solve for .

Explanation:

1) Begin the problem by factoring the final term. Include the negative when factoring.

–2 + 2 = 0

–4 + 1 = –3

–1 + 4 = 3

All options are exhausted, therefore the problem cannot be solved by factoring, which means that the roots either do not exist or are not rational numbers. We must use the quadratic formula.

### Example Question #23 : Quadratic Formula

Explanation:

The standard form of a quadratic equation is , where a,b, and c are constants. Plug these constants into the quadratic formula to solve for x.

### Example Question #24 : Quadratic Formula

Solve for  by using the quadratic formula:

None of the above

Explanation:

From here you just plug in your numbers, so:

Simplify:

Then you need to simplify the inside looking for perfect squares:

### Example Question #25 : Quadratic Formula

Use the quadratic formula to solve the equation

Explanation:

### Example Question #26 : Quadratic Formula

Find the zeros of ?

Explanation:

This specific function cannot be factored, so use the quadratic equation:

Our function is in the form  where,