Question

Write the following equation in the form \(ax^2 + bx + c = 0\), then write the values of \(a, b, c\):
\[ 2y = 10 - y^2 \]

Hint:

To convert any equation into standard quadratic form, move all terms to one side and simplify so that one side equals zero.

Answer 1

Step 1: Write the given equation.
\[ 2y = 10 - y^2 \] Step 2: Bring all terms to one side.
\[ y^2 + 2y - 10 = 0 \] Step 3: Compare with the standard quadratic form.
The standard quadratic equation is \[ ax^2 + bx + c = 0 \] By comparison, we get \[ a = 1, \quad b = 2, \quad c = -10 \] Step 4: Conclusion.
Hence, the equation in standard form is \(y^2 + 2y - 10 = 0\) with \[ a = 1, \; b = 2, \; c = -10 \] Final Answer: \[ \boxed{a = 1, \; b = 2, \; c = -10} \]