Quadratic Function Practice Problems - Parabola Vertex & Graph

The quadratic equation in the problem is already arranged (meaning all terms are on one side and 0 on the other side), so let's proceed to answer the question asked:

The question asked in the problem - What is the value of the coefficient$a$ in the equation?

Let's recall the definitions of coefficients in solving quadratic equations and the roots formula:

The rule states that the roots of an equation of the form:

$ax^2+bx+c=0$are:

$x_{1,2}=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

That is the coefficient $a$is the coefficient of the quadratic term (meaning the term with the second power)- $x^2$Let's examine the equation in the problem:

$$$-x^2+7x-9 =0$

Remember that the minus sign before the quadratic term means multiplication by: $-1$ , therefore- we can write the equation as:

$-1\cdot x^2+7x-9 =0$

The number that multiplies the $x^2$, is $-1$ hence we identify that the coefficient of the quadratic term is the number $-1$,

Therefore the correct answer is A.

The quadratic equation of the given problem is already arranged (that is, all the terms are found on one side and the 0 on the other side), thus we approach the given problem as follows;

In the problem, the question was asked: what is the value of the coefficient$b$in the equation?

Let's remember the definitions of coefficients when solving a quadratic equation as well as the formula for the roots:

The rule says that the roots of an equation of the form

$ax^2+bx+c=0$are :

$x_{1,2}=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

That is the coefficient$b$is the coefficient of the term in the first power -$x$We then examine the equation of the given problem:

$$$3x^2+8x-5 =0$That is, the number that multiplies

$x$ is

$8$Consequently we are able to identify b, which is the coefficient of the term in the first power, as the number$8$,

Thus the correct answer is option d.

The quadratic equation is given as $4x^2 + 9x - 2$. This equation is in the standard form of a quadratic equation, which is $ax^2 + bx + c$, where $a$, $b$, and $c$ are coefficients.

• The term $4x^2$ indicates that the coefficient $a = 4$.
• The term $9x$ indicates that the coefficient $b = 9$.
• The constant term $-2$ indicates that the coefficient $c = -2$.

From this analysis, we can see that the coefficient $c$ is $-2$.

Therefore, the value of the coefficient $c$ in the equation is $-2$.

The quadratic equation of the given problem has already been arranged (that is, all the terms are on one side and 0 is on the other side) thus we can approach the question as follows:

In the problem, the question was asked: what is the value of the coefficient$c$in the equation?

Let's remember the definition of a coefficient when solving a quadratic equation as well as the formula for the roots:

The rule says that the roots of an equation of the form

$ax^2+bx+c=0$are:

$x_{1,2}=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

That is the coefficient
$c$is the free term - and as such the coefficient of the term is raised to the power of zero -$x^0$(Any number other than zero raised to the power of zero equals 1:

$x^0=1$)

Next we examine the equation of the given problem:

$$$3x^2+5x=0$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:

$3x^2+5x+0=0$and therefore the value of the coefficient$c$ is 0.

Hence the correct answer is option c.

To solve this problem, we will identify the parameters of the given quadratic function step-by-step:

• Step 1: Define the problem statement: We have $y = x^2 + x + 5$.
• Step 2: Identify the standard form of a quadratic function, which is $y = ax^2 + bx + c$.
• Step 3: Compare the given quadratic expression with the standard form to identify the coefficients.

Now, let's analyze the quadratic function provided:

From the given expression $y = x^2 + x + 5$:
- The coefficient of $x^2$ is $1$, so $a = 1$.
- The coefficient of $x$ is $1$, so $b = 1$.
- The constant term is $5$, so $c = 5$.

Therefore, the parameters of the quadratic function are $a = 1$, $b = 1$, and $c = 5$.

Consequently, the correct choice from the provided options is $(a = 1, b = 1, c = 5)$.