What are points a, b, c using standard form of the quadratic equation for these three points: (4, -8) (3, -2) (5, -1) 

We are given three points: \( (4, -8) \), \( (3, -2) \), and \( (5, -1) \), and we need to determine the quadratic equation passing through these points in standard form:

\[
y = ax^2 + bx + c
\]

To find \( a \), \( b \), and \( c \), we will set up a system of equations by plugging in each point into the general quadratic form. Let's do this step by step.

1. For \( (4, -8) \):
   \[
   -8 = a(4)^2 + b(4) + c \quad \Rightarrow \quad 16a + 4b + c = -8
   \]

2. For \( (3, -2) \):
   \[
   -2 = a(3)^2 + b(3) + c \quad \Rightarrow \quad 9a + 3b + c = -2
   \]

3. For \( (5, -1) \):
   \[
   -1 = a(5)^2 + b(5) + c \quad \Rightarrow \quad 25a + 5b + c = -1
   \]

Now, we have the system of equations:

\[
\begin{aligned}
16a + 4b + c &= -8 \\
9a + 3b + c &= -2 \\
25a + 5b + c &= -1 \\
\end{aligned}
\]

We can solve this system of equations to find \( a \), \( b \), and \( c \).

I'll calculate that for you.

What are points a, b, c using standard form of the quadratic equation for these three points: (4, -8) (3, -2) (5, -1)?

Discover how to find the coefficients a, b, and c for a quadratic equation passing through the points (4, -8), (3, -2), and (5, -1). This step-by-step solution explains key algebraic concepts like quadratic equations and systems of equations. Ideal for students in Grades 9-11.

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