Quadratic Equations Practice Problems - Solve by 3 Methods

Let's recall the general form of the quadratic function:

$y=ax^2+bx+c$ The function given in the problem is:

$y=-x^2+25x$$c$is the free term (meaning the coefficient of the term with power 0),

In the function in the problem there is no free term,

Therefore, we can identify that:

$c=0$Therefore, the correct answer is answer A.

To solve this problem, we'll follow these steps:

• Identify the given information and the standard quadratic form
• Compare the given equation to this standard form
• Extract the coefficients $a$, $b$, and $c$ and find $b$

Now, let's work through each step:
Step 1: The problem provides us with the equation $y = 4x^2 - 16$. It's already in a form where we can identify the coefficients.
Step 2: Recall the standard form of a quadratic equation is $ax^2 + bx + c$. Compare this form to the equation $y = 4x^2 - 16$.
Step 3: By comparison, the coefficient of $x^2$ (which is $a$) is 4. There is no $x$ term explicitly present, implying that $b = 0$. The constant $c$ is -16.
Therefore, after comparison and identification, it becomes clear that the value of $b$ in the equation is $b = 0$.

To solve this problem, we'll follow these steps:

• Step 1: Compare the given equation $y = 5 + 3x^2$ to the standard form $ax^2 + bx + c$.
• Step 2: Identify the terms corresponding to $a$, $b$, and $c$.

Now, let's work through each step:
Step 1: The given equation is $y = 5 + 3x^2$. Rearranging it in the standard form, we have $y = 3x^2 + 0\cdot x + 5$.

Step 2: From this arrangement, it's clear that:
- $a = 3$ (the coefficient of $x^2$)
- $b = 0$ (there is no $x$ term, so its coefficient is 0)
- $c = 5$ (the constant term)

Therefore, the value of $c$ is $\ c=5$.

To solve this problem, we need to identify the coefficient of $x$ in the given quadratic equation. The equation given is $y = 3x^2 + 10 - x$. Let’s rearrange this equation to match the standard form of a quadratic equation $ax^2 + bx + c$.

The given equation can be rewritten as:

$y = 3x^2 - x + 10$

Here, we can identify the coefficients:

• $a = 3$ (for $x^2$)
• $b = -1$ (for $x$)
• $c = 10$ (the constant term)

Therefore, the value of $b$, the coefficient of $x$, is $-1$.

To solve this problem, we'll follow these steps:

• Step 1: Rewrite the given equation in standard quadratic form if necessary.
• Step 2: Identify the term with $x^2$ in the equation.
• Step 3: Extract the coefficient of $x^2$ as $a$.

Now, let's work through each step:
Step 1: The provided equation is $y = 3x - 10 + 5x^2$. Although it's not initially in standard form, observation shows that the $x^2$ term is clearly present.
Step 2: Locate the $x^2$ term: in our equation, this term is $5x^2$.
Step 3: The coefficient of $x^2$ is $5$. Hence, $a = 5$.

Therefore, the coefficient of $x^2$, or $a$, is $a = 5$.