Solve quadratic equations using the quadratic formula
Use the discriminant to predict the number of solutions of a quadratic equation
Identify the most appropriate method to use to solve a quadratic equation
Before you get started, take this readiness quiz.
Simplify:
.
If you missed this problem, review
[link] .
Simplify:
.
If you missed this problem, review
[link] .
Simplify:
.
If you missed this problem, review
[link] .
When we solved quadratic equations in the last section by completing the square, we took the same steps every time. By the end of the exercise set, you may have been wondering ‘isn’t there an easier way to do this?’ The answer is ‘yes.’ In this section, we will derive and use a formula to find the solution of a quadratic equation.
We have already seen how to solve a formula for a specific variable ‘in general’ so that we would do the algebraic steps only once and then use the new formula to find the value of the specific variable. Now, we will go through the steps of completing the square in general to solve a quadratic equation for
x . It may be helpful to look at one of the examples at the end of the last section where we solved an equation of the form
as you read through the algebraic steps below, so you see them with numbers as well as ‘in general.’
This last equation is the Quadratic Formula.
Quadratic formula
The solutions to a quadratic equation of the form
,
are given by the formula:
To use the Quadratic Formula, we substitute the values of
into the expression on the right side of the formula. Then, we do all the math to simplify the expression. The result gives the solution(s) to the quadratic equation.
How to solve a quadratic equation using the quadratic formula
Solve a quadratic equation using the quadratic formula.
Write the Quadratic Formula in standard form. Identify the
,
, and
values.
Write the Quadratic Formula. Then substitute in the values of
,
, and
Simplify.
Check the solutions.
If you say the formula as you write it in each problem, you’ll have it memorized in no time. And remember, the Quadratic Formula is an equation. Be sure you start with ‘
’.
Step 1: Find the mean. To find the mean, add up all the scores, then divide them by the number of scores. ...
Step 2: Find each score's deviation from the mean. ...
Step 3: Square each deviation from the mean. ...
Step 4: Find the sum of squares. ...
Step 5: Divide the sum of squares by n – 1 or N.
The sample of 16 students is taken. The average age in the sample was 22 years with astandard deviation of 6 years. Construct a 95% confidence interval for the age of the population.
Bhartdarshan' is an internet-based travel agency wherein customer can see videos of the cities they plant to visit. The number of hits daily is a normally distributed random variable with a mean of 10,000 and a standard deviation of 2,400
a. what is the probability of getting more than 12,000 hits?
b. what is the probability of getting fewer than 9,000 hits?
Bhartdarshan'is an internet-based travel agency wherein customer can see videos of the cities they plan to visit. The number of hits daily is a normally distributed random variable with a mean of 10,000 and a standard deviation of 2,400.
a. What is the probability of getting more than 12,000 hits