Quadratic Function Practice Problems - Parabola Vertex & Graph

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.

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.

Let's determine the coefficients for the quadratic function given by $y = -2x^2 + 3x + 10$.

• Step 1: Identify $a$.
  The coefficient of $x^2$ is $-2$. Thus, $a = -2$.
• Step 2: Identify $b$.
  The coefficient of $x$ is $3$. Thus, $b = 3$.
• Step 3: Identify $c$.
  The constant term is $10$. Thus, $c = 10$.

Comparing these coefficients to the provided choices, the correct answer is:

$a = -2, b = 3, c = 10$ .

Therefore, the correct choice is Choice 4.

The given quadratic function is $y = 5x^2 - 4x - 30$.
To identify the coefficients, let's compare this with the standard form of a quadratic equation, $y = ax^2 + bx + c$.

• Step 1: Compare the terms of the given equation to the standard form.
• Step 2: Identify each coefficient:
  For $ax^2$, $a = 5$ in the term $5x^2$.
  For $bx$, $b = -4$ in the term $-4x$.
  For the constant term $c$, $c = -30$.

Thus, we have identified the coefficients as $a = 5$, $b = -4$, and $c = -30$.

Therefore, the correct answer is $a = 5, b = -4, c = -30$.

The correct choice is .

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.