Quadratic Equations Practice Problems - Solve by 3 Methods

To identify the coefficients from the quadratic equation $5x^2 + 6x - 8 = 0$, follow these steps:

• Standard Form of Quadratic Equation: Compare $5x^2 + 6x - 8$ with the standard form $ax^2 + bx + c = 0$.
• Identify $a$, $b$, and $c$:
  • $a = 5$: The coefficient of $x^2$.
  • $b = 6$: The coefficient of $x$.
  • $c = -8$: The constant term (independent of $x$).

Therefore, from the equation $5x^2 + 6x - 8 = 0$, the coefficients are identified as $a=5$, $b=6$, and $c=-8$.

Comparing with choices, we find that choice 2 is correct: $a=5$, $b=6$, $c=-8$.

Thus, the coefficients are identified as $a=5$, $b=6$, $c=-8$.

The parameters are expressed in the quadratic equation as follows:

aX2+bX+c=0

We substitute into the formula:

-5±√(5²-4*1*4) 
          2

-5±√(25-16)
         2

-5±√9
    2

-5±3
   2

The symbol ± means that we have to solve this part twice, once with a plus and a second time with a minus,

This is how we later get two results.

-5-3 = -8
-8/2 = -4

-5+3 = -2
-2/2 = -1

And thus we find out that X = -1, -4

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 $a = 5$.

To determine the coefficient $a$ in the given quadratic equation $y = -x^2 - 3x + 1$, follow these steps:

• Step 1: Recognize the form of the quadratic equation as $y = ax^2 + bx + c$.
• Step 2: Identify the $x^2$ term in the equation $y = -x^2 - 3x + 1$.
• Step 3: Determine the coefficient of the $x^2$ term, which is in front of $x^2$.

In the equation $y = -x^2 - 3x + 1$, the term involving $x^2$ is $-x^2$, where the coefficient $a$ is clearly $-1$.

Hence, the value of $a$ is $a = -1$.

To solve this problem, we need to identify the coefficients in the given quadratic equation:

• The equation provided is $y = 2x - 3x^2 + 1$.
• The standard form of a quadratic equation is $ax^2 + bx + c$.
• From the equation, identify:
  • The $ax^2$ term is $-3x^2$, indicating $a = -3$.
  • The $bx$ term is $2x$, indicating $b = 2$.
  • The constant term $c$ is $1$.

Thus, the coefficient $b$ in the equation $y = 2x - 3x^2 + 1$ is $b = 2$, which corresponds to choice 1.