https://r2.erweima.ai/mathbot/image/172643986292233up3e4y.jpg

The image presents a parabola and asks for its equation in three different forms based on the points labeled \( A \left( \frac{-17}{20}, \frac{-169}{32} \right) \) and \( B \left( 2, \frac{-61}{50} \right) \).

We can find the equation of the parabola in three common forms:

1. **Standard form**: \( y = ax^2 + bx + c \)
2. **Vertex form**: \( y = a(x - h)^2 + k \)
3. **Factored form** (if the roots are known): \( y = a(x - r_1)(x - r_2) \)

### Step 1: Standard Form
We use the given points \( A \) and \( B \) to find the equation in the standard form. The points provide specific \( (x, y) \) pairs that we can substitute into the equation \( y = ax^2 + bx + c \).

Let me calculate the equation for you by finding the values of \( a \), \( b \), and \( c \) based on these points.

Let’s begin with that.The system of equations yields the following relationships between \( a \), \( b \), and \( c \):

\[
a = -0.5882c - 2.3941
\]
\[
b = 0.6765c + 4.1782
\]

To fully determine the values of \( a \), \( b \), and \( c \), we need one more point or condition, such as a vertex or another given coordinate. Based on the diagram, it looks like point \( A \) might represent the vertex of the parabola, given its location at the minimum point.

Should I proceed by assuming that point \( A \) is the vertex and solve accordingly?

Determine l'équation de la parabole sous ses trois différentes formes à partir des points A(-17/20, -169/32) et B(2, -61/50).

Learn how to find the equation of a parabola in standard, vertex, and factored forms using the points A(-17/20, -169/32) and B(2, -61/50). This solution covers quadratic functions, the vertex theorem, and algebraic methods.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation