The Parabola
This function is a quadratic function and is called a parabola.
We will focus on two main types of parabolas: maximum and minimum parabolas.
This function is a quadratic function and is called a parabola.
We will focus on two main types of parabolas: maximum and minimum parabolas.
Also called smiling or happy.
A vertex is the minimum point of the function, where is the lowest.
We can identify that it is a minimum parabola if the equation is positive.
Also called sad or crying.
A vertex is the maximum point of the function, where is the highest.
We can identify that it is a maximum parabola if the equation is negative.
To the parabola,
the vertex marks its highest point.
How do we find it?
\( y=x^2+10x \)
\( y=2x^2-5x+6 \)
What is the value of the coefficient \( b \) in the equation below?
\( 3x^2+8x-5 \)
What is the value of the coefficient \( c \) in the equation below?
\( 3x^2+5x \)
\( y=x^2 \)
Here we have a quadratic equation.
A quadratic equation is always constructed like this:
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.
a is the coefficient of X², here it does not have a coefficient, therefore
is the number that comes before the X that is not squared.
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.
What is the value of the coefficient in the equation below?
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 coefficientin 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
are :
That is the coefficientis the coefficient of the term in the first power -We examine the equation of the problem:
That is, the number that multiplies
is
And then we recognize b, which is the coefficient of the term in the first power, is the number,
The correct answer is option d.
8
What is the value of the coefficient in the equation below?
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 coefficientin 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
are:
That is the coefficient
is the free term - that is, the coefficient of the term raised to the power of zero -(And this is because any number other than zero raised to the power of zero equals 1:
)
We examine the equation of the problem:
Note 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:
and therefore the value of the coefficient is 0.
The correct answer is option c.
0
\( y=x^2-6x+4 \)
\( y=2x^2-3x-6 \)
\( y=-2x^2+3x+10 \)
\( y=3x^2+4x+5 \)
What is the value ofl coeficiente \( a \) in the equation?
\( -x^2+7x-9 \)
What is the value ofl coeficiente in the equation?
-1
What is the value of the coefficient \( c \) in the equation below?
\( 4x^2+9x-2 \)
\( y=x^2+x+5 \)
\( y=-x^2+x+5 \)
\( y=4+3x^2-x \)
\( y=3x^2+4-5x \)
What is the value of the coefficient in the equation below?
-2