https://file.aiquickdraw.com/mathbot/file/1725787848960aevr93c8.jpg

The equation of the curve is given in the image as:

\[
y = -mx^2 + \frac{m}{2}x + c
\]

where \( m \) and \( c \) are integers. We are also given a point on the curve, \( \left(1, \frac{7}{8}\right) \), labeled as \( A \).

To find the values of \( c + m \), we can substitute the point \( (1, \frac{7}{8}) \) into the equation of the curve and solve for \( m \) and \( c \).

The equation becomes:

\[
\frac{7}{8} = -m(1)^2 + \frac{m}{2}(1) + c
\]
\[
\frac{7}{8} = -m + \frac{m}{2} + c
\]

Next, we simplify this equation and solve for \( m \) and \( c \). I will now calculate this.We have the solution for \( c \) in terms of \( m \) as:

\[
c = \frac{m}{2} + \frac{7}{8}
\]

Since both \( m \) and \( c \) are integers, \( \frac{m}{2} + \frac{7}{8} \) must also be an integer. To satisfy this condition, \( m \) must be chosen such that the sum is an integer.

Let me now find the integer values of \( m \) and \( c \) that satisfy this condition.It seems like I can’t do more advanced data analysis right now. Please try again later.

Would you like to continue manually or upload another question?

Based on the query submitted by the user and the corresponding solution, generate the following information in JSON format: Determine the values of c and m given the quadratic equation y = -mx^2 + (m/2)x + c and a point on the curve (1, 7/8).

Explore how to find integer solutions for the quadratic equation y = -mx^2 + (m/2)x + c at the point (1, 7/8). This advanced problem requires understanding algebra and the properties of quadratic equations.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation