What is qudric factorising
pls help
Factoring quadratics means finding two binomials that when multiplied together give you the original quadratic expression. For example, to factor the quadratic expression x^2 + 5x + 6, you would look for two binomials in the form (x + ___)(x + ___) that, when multiplied together using FOIL, give you x^2 + 5x + 6.
To do this, you would need to find two numbers that multiply to give you 6 (the constant term in the expression) and add to give you 5 (the coefficient of the x term). In this case, those numbers are 2 and 3. So, you can factor x^2 + 5x + 6 as (x + 2)(x + 3).
There are other methods for factoring quadratics depending on their form, such as using completing the square or using the quadratic formula, but factoring using the method described above is a common and useful way to factor quadratics.
I don't get can you please explain it to me
Sure, let me explain it step-by-step.
The general form of a quadratic expression is given by:
ax^2 + bx + c
where a, b, and c are constants and x is a variable.
To factorize this quadratic expression, we want to write it in the form:
a(x - r)(x - s)
where r and s are constants. This gives us two binomials multiplied together, (x - r) and (x - s), which when expanded using FOIL, give us the original quadratic expression.
Here's how we can factorize a quadratic expression:
Step 1: Write the quadratic expression in the form ax^2 + bx + c.
Step 2: Find two constants r and s such that r x s = c and r + s = b.
Example: Let's say we want to factorize the quadratic expression 2x^2 + 5x + 3.
In this case, we need to find two numbers r and s such that:
r x s = 2 x 3 = 6
r + s = 5
One way to do this is to list all the factors of 6 that add up to 5. We see that the factors are 2 and 3. Therefore, we can write:
2x^2 + 5x + 3 = 2(x + 3)(x + 1/2)
This is the factored form of the quadratic expression.
Note that in this example, we multiplied the constant term (3) by the coefficient of the x^2 term (2) to get 6. This tells us that the constant term (3) is the product of the constant terms in the two binomials of the factored form.
what does ax^2 + bx + c mean
ax^2 + bx + c is a quadratic expression, where a, b, and c are constants and x is a variable.
The term ax^2 is the quadratic term. The coefficient a tells us whether the parabola opens up or down. If a is positive, the parabola opens up, and if a is negative, the parabola opens down.
The term bx is the linear term. The coefficient b tells us how steep the parabola is (or how fast it rises). If the value of b is positive, the parabola will slope upwards, and if it's negative, the parabola will slope downwards.
The constant term c is the y-intercept, which tells us where the parabola intersects the y-axis.
Together, these three terms define a quadratic function, which is a type of polynomial function in one variable.
Man i don't get this :(
I understand that it can be a bit confusing, but let me try to explain it in a different way.
A quadratic expression is an expression that can be written in the form:
ax^2 + bx + c
Here, the variable is x and a, b, and c are constants (numbers).
The term ax^2 is a quadratic term, which means that it has a power of 2. This term gives us information about the shape of the graph of the quadratic function. Specifically, if a is positive, the graph will be U-shaped with a minimum point, and if a is negative, the graph will be upside-down with a maximum point.
The term bx is a linear term, which means that it has a power of 1. This term gives us information about the slope of the graph of the quadratic function. Specifically, if b is positive, the graph will slope upwards to the right, and if b is negative, the graph will slope downwards to the right.
The term c is a constant term, which means that it has a power of 0. This term gives us information about where the graph of the quadratic function intersects the y-axis.
So, when you see an expression like ax^2 + bx + c, you can think of it as a function that takes x as an input and gives you an output (y). The shape of the graph, the slope of the graph, and where the graph intersects the y-axis can be determined from the constants a, b, and c.