𝒚 = 𝟔𝒙𝟐 − 𝟏𝟗𝒙 + 𝟏0 

The equation you provided is a quadratic function:

\[
y = 6x^2 - 19x + 10
\]

### Key Points about this Quadratic Function:

1. **Standard Form**: The equation is in the standard form \( y = ax^2 + bx + c \), where:
   - \( a = 6 \)
   - \( b = -19 \)
   - \( c = 10 \)

2. **Vertex**: The vertex of the parabola (the highest or lowest point) is given by the formula for \(x\)-coordinate:

   \[
   x = \frac{-b}{2a}
   \]

   Substituting \( a = 6 \) and \( b = -19 \):

   \[
   x = \frac{-(-19)}{2(6)} = \frac{19}{12}
   \]

   For the \(y\)-coordinate, substitute \( x = \frac{19}{12} \) into the original equation to find the value of \( y \).

3. **Axis of Symmetry**: The axis of symmetry is the vertical line through the vertex, given by \( x = \frac{19}{12} \).

4. **Direction of the Parabola**: Since \( a = 6 \), which is positive, the parabola opens **upwards**.

5. **Y-intercept**: The y-intercept occurs when \( x = 0 \). Substituting \( x = 0 \) into the equation:

   \[
   y = 6(0)^2 - 19(0) + 10 = 10
   \]

   So the y-intercept is \( (0, 10) \).

Would you like more details or help solving for specific values of \( y \)?

### Related Questions:
1. How do you find the x-intercepts of this quadratic equation?
2. What is the domain and range of this quadratic function?
3. How do you complete the square for this equation?
4. How do you determine the maximum or minimum value of this quadratic?
5. How does changing the value of \( a \) affect the shape of the parabola?

**Tip**: The discriminant \( \Delta = b^2 - 4ac \) helps determine the number of real roots a quadratic has.

𝒚 = 𝟔𝒙𝟐 − 𝟏𝟗𝒙 + 𝟏0

Learn how to solve the quadratic equation 6x^2 - 19x + 10 with step-by-step guidance. This problem includes finding the vertex, axis of symmetry, and y-intercept, using key algebraic formulas. Suitable for Grades 9-11 students.

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