Lesson video

Hi, I'm Miss Davies.

In this lesson, we're going to be using the quadratic formula to solve quadratic equations.

A quadratic function can be written in the form of axe squared add bx add c, where the value of a does not equal zero.

In this form, the values of a and b are the coefficients of x squared and x.

Coefficient means the multiple of the variable.

a is the value that x squared is being multiplied by, and b is the value that x is being multiplied by, c is the constant.

In the expression x squared add 7x add five, the x squared coefficient is one, the x coefficient is seven, and the constant is five.

In the expression 4x squared squared subtract 3x, the x squared coefficient is four, the x coefficient is negative three, and the constant is zero.

In the expression negative 35 subtract x squared add 20x, the a value is negative one, the b value is 20, and the c value is negative 35.

Here's some questions for you to try.

Pause the video to complete your task and resume once you're finished.

Here are the answers.

Remember that the value for a is the x squared coefficient, b is the x coefficient, and c is the constant which is the number that is on its own.

The order of the terms doesn't matter.

The quadratic formula is used to solve a quadratic equation that is in the form axe squared add bx add c is equal to zero.

The quadratic formula is that x is equal to negative b add or subtract the square root of b squared subtract 4ac, and this is all divided by 2a.

a and b are the coefficients of x squared and x, and c represents the constant.

In this example, we're going to solve the equation x squared add 6x add eight is equal to zero using the quadratic formula.

Looking at this equation, we know that the value of a is one, the value of b is six, and the value of c is eight.

If we substitute these three values into the quadratic equation, we get this.

We can then type this into a calculator to find that x is equal to negative two or x is equal to negative four.

Here's some questions for you to try, pause the video to complete your task and resume once you're finished.

Here are the answers.

If you don't have this solutions, check the calculations that you typed into your calculator to make sure that they were correct.

In this next example, we've been asked to solve the equation 3x squared add 7x subtract five is equal to zero using the quadratic formula.

We've been instructed to give the solution to one decimal place.

We can see from the equation that our a value is three, our b value is seven, and our c value is negative five.

If we substitute these into the formula we get this.

We can simplify this down to x is equal to negative seven add or subtract the square root of 109 divided by six.

By typing this into the calculator, we can get the solutions of x is equal to negative 0.

6 or x is equal to negative 2.

2.

Both of these solutions are to one decimal place.

Here's some questions for you to try, pause the video to complete your tasks and resume once you're finished.

Here were the answers.

Make sure that all of your solutions are given to one decimal place as this was specified in the question.

But this next equation, it isn't written equal to zero.

First thing that we need to do is rearrange the equation so that we've got an equation that is equal to zero.

To do this, we can subtract 21 from both sides.

This then tells us that the value for a is three, the value for b is seven, and the value for c is negative 21.

We can then substitute this into a quadratic formula.

Simplifying this down gives us the x is equal to negative seven add or subtract square root 301, all divided by six.

By then typing the two calculations into a calculator, we get the solution of x is equal to negative 1.

72, or x is equal to negative 4.

06.

Both of these solutions are correct to two decimal places.

Here's some questions for you to try, pause the video to complete your task and resume once you're finished.

Here are the answers.

Your first step in solving both of these equations should have been to make them equal to zero before finding the values of a, b and c.

Here is a question for you to try, pause the video to complete your task and resume once you're finished.

Here is the answer, to solve this equation your first step should have been to expand and simplify both sides of the equal symbol.

Then you can find the values of a, b and c to substitute into the quadratic formula.

That's all for this lesson, thanks for watching.