To determine the high or low point (vertex) of the parabola defined by the quadratic equation \( y = -6x^2 + 3x + 8 \), we can analyze the given equation. Since the quadratic term has a negative coefficient (\(-6\)), we know the parabola opens downward, indicating that the vertex will be the high point.
To find the x-coordinate of the vertex, we can use the formula:
\[ x = -\frac{b}{2a} \]
where \( a = -6 \) and \( b = 3 \).
Substituting these values into the formula:
\[ x = -\frac{3}{2 \cdot -6} = -\frac{3}{-12} = \frac{1}{4} = 0.25 \]
Now, we can substitute \( x = 0.25 \) back into the equation to find the corresponding y-coordinate:
\[ y = -6(0.25)^2 + 3(0.25) + 8 \] \[ y = -6(0.0625) + 0.75 + 8 \] \[ y = -0.375 + 0.75 + 8 \] \[ y = 0.375 + 8 \] \[ y = 8.375 \]
Thus, the vertex of the parabola is at \( (0.25, 8.375) \), which is the high point because the parabola opens downward.
From the options given:
- \( (0.5, 9) \) is the high point on the parabola.
- \( (-1, -1) \) is the low point on the parabola.
- \( (0.25, 8.375) \) is the high point on the parabola.
- \( (0.25, 8.375) \) is the low point on the parabola.
The correct response is:
\( (0.25, 8.375) \) is the high point on the parabola.
1 answer