examples with solutions for the quadratic function
Exercise #1
y=x2+10x
Video Solution
Step-by-Step Solution
Here we have a quadratic equation.
A quadratic equation is always constructed like this:
y=ax2+bx+c
Where a, b, and c are generally already known to us, and the X and Y points need to be discovered.
Firstly, it seems that in this formula we do not have the C,
Therefore, we understand it is equal to 0.
c=0
a is the coefficient of X², here it does not have a coefficient, therefore
a=1
b=10
is the number that comes before the X that is not squared.
Answer
a=1,b=10,c=0
Exercise #2
y=2x2−5x+6
Video Solution
Step-by-Step Solution
In fact, a quadratic equation is composed as follows:
y = ax²-bx-c
That is,
a is the coefficient of x², in this case 2. b is the coefficient of x, in this case 5. And c is the number without a variable at the end, in this case 6.
Answer
a=2,b=−5,c=6
Exercise #3
What is the value of the coefficient b in the equation below?
3x2+8x−5
Video Solution
Step-by-Step Solution
The quadratic equation of the problem is already arranged (that is, all the terms on one side and 0 on the other side), so we approach answering the question posed:
In the problem, the question was asked: what is the value of the coefficientbin the equation?
Let's remember the definitions of the coefficients when solving a quadratic equation and the formula for the roots:
The rule says that the roots of an equation of the form
ax2+bx+c=0are :
x1,2=2a−b±b2−4ac
That is the coefficientbis the coefficient of the term in the first power -xWe examine the equation of the problem:
3x2+8x−5=0That is, the number that multiplies
x is
8And then we recognize b, which is the coefficient of the term in the first power, is the number8,
The correct answer is option d.
Answer
8
Exercise #4
What is the value of the coefficient c in the equation below?
3x2+5x
Video Solution
Step-by-Step Solution
The quadratic equation of the problem is already ordered (that is, all the terms on one side and 0 on the other side), so we approach answering the question posed:
In the problem, the question was asked: what is the value of the coefficientcin the equation?
Let's remember the definitions of the coefficients when solving a quadratic equation and the formula for the roots:
The rule says that the roots of an equation of the form
ax2+bx+c=0are:
x1,2=2a−b±b2−4ac
That is the coefficient cis the free term - that is, the coefficient of the term raised to the power of zero -x0(And this is because any number other than zero raised to the power of zero equals 1:
x0=1)
We examine the equation of the problem:
3x2+5x=0Note that there is no free term in the equation, that is, the numerical value of the free term is 0, in fact the equation can be written as follows:
3x2+5x+0=0and therefore the value of the coefficientc is 0.