Quadratic Formula
Quadratic Formula
A quadratic expression is an expression that takes the form of ax2 + bx + c. Some examples of quadratic expressions are
2x2 + 6x + 12x2 + 3x -12 9x2 + 5x + 2x2 -25
So the above are examples of quadratic expressions, to describe a quadratic expression we would say that it contains an x2 term, an x term and a constant (the number by itself); c stands for constant.
One thing you have to understand is that a quadratic expression is a quadratic expression because it contains the ax2 term. For an expression to be quadratic, it does not need to contain the bx term and c term, but it has to contain the ax2 .
So a quadratic expression, as mentioned above, takes form of ax2 + bx + c.
a can be any number except 0b can be any numberc can be any number
Be careful, sometimes the equation can be quadratic in an exam, however you make the mistake of not identifying that it is indeed a quadratic equation.
Watch video 1 to see some examples.
In the quadratic expression x2 + 3x - 12, the constant is -12.
Let's say we need to solve a general quadratic equation as shown below.
ax2 + bx + c = 0
This means that we are trying to find the value(s) of x, so that when we substitute the x, in the expression, with a value or values, the quadratic expression equals 0. To find the values of x, we use the quadratic formula. This is shown in video 2.
When we need to solve for x, given a quadratic equation, ONE METHOD to solve for x is by using the quadratic formula as shown in video 2.
It is a simple matter of substitution. If you do not know how to substitute, learn this first. It is not hard, check the substitution page.
You cannot use this formula to find x, as shown in video 2, if the expression that is equal to 0 is not quadratic AND/OR if the quadratic expression is not equal to 0. The quadratic formula only solves for x when the quadratic expression is equal to 0.
2x2 + 6x + 12x2 + 3x -12 9x2 + 5x + 2x2 -25
So the above are examples of quadratic expressions, to describe a quadratic expression we would say that it contains an x2 term, an x term and a constant (the number by itself); c stands for constant.
One thing you have to understand is that a quadratic expression is a quadratic expression because it contains the ax2 term. For an expression to be quadratic, it does not need to contain the bx term and c term, but it has to contain the ax2 .
So a quadratic expression, as mentioned above, takes form of ax2 + bx + c.
a can be any number except 0b can be any numberc can be any number
Be careful, sometimes the equation can be quadratic in an exam, however you make the mistake of not identifying that it is indeed a quadratic equation.
Watch video 1 to see some examples.
In the quadratic expression x2 + 3x - 12, the constant is -12.
Let's say we need to solve a general quadratic equation as shown below.
ax2 + bx + c = 0
This means that we are trying to find the value(s) of x, so that when we substitute the x, in the expression, with a value or values, the quadratic expression equals 0. To find the values of x, we use the quadratic formula. This is shown in video 2.
When we need to solve for x, given a quadratic equation, ONE METHOD to solve for x is by using the quadratic formula as shown in video 2.
It is a simple matter of substitution. If you do not know how to substitute, learn this first. It is not hard, check the substitution page.
You cannot use this formula to find x, as shown in video 2, if the expression that is equal to 0 is not quadratic AND/OR if the quadratic expression is not equal to 0. The quadratic formula only solves for x when the quadratic expression is equal to 0.
Video 2 Explanation
Video 2 Explanation
Question: Solve for x in 2x2 + 6x + 3 = 0
So first we MUST check whether 2x2 + 6x + 3 is in the form of ax2 + bx + c. Yes it is and a = 2, b = 6 and c = 3.
Then we substitute a, b and c with their respective values in the quadratic formula as seen in the video.
We find that there are 2 solutions. You will understand why there are two solutions for this specific quadratic equation when you understand how a quadratic equation looks like on a graph, but let's also understand why there are two solutions using the formula.
The formula contains a square root part. When we square root a number, there are always two solutions. For example, the square root of 4 is 2 AND -2.
2 x 2 = 4
-2 x -2 = 4 (A negative number multiplied by a negative number is a positive number)
As a result, that is why we can add and subtract the square root part, thus we gain two answers, watch the video to see the answers.
Video 1
Video 1
The answer for question in the video is b and c.
Video 2
Video 2