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3. \( y=-3 x^{2}+12 x+2 \)

Ask by Schofield Munoz. in the Philippines
Mar 11,2025

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The quadratic function \( y = -3x^2 + 12x + 2 \) has a vertex at \( (2, 14) \), an axis of symmetry at \( x = 2 \), a y-intercept at \( (0, 2) \), and x-intercepts at \( \left(2 - \frac{\sqrt{42}}{3}, 0\right) \) and \( \left(2 + \frac{\sqrt{42}}{3}, 0\right) \).

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The Deep Dive

Did you know that the equation \( y=-3x^2+12x+2 \) represents a downward-opening parabola? This is due to the negative coefficient of the \( x^2 \) term, which gives it a "frown" shape. Among the many properties of parabolas, the vertex represents either a maximum or a minimum point—in this case, it’s the maximum since our parabola opens downward. To find the vertex, you can use the vertex formula \( x = -\frac{b}{2a} \). Plugging in values from our equation where \( a = -3 \) and \( b = 12 \), you'll discover that the x-coordinate of the vertex is at 2. After substituting back into the equation, you can find the maximum y-value to complete your parabolic journey. Happy graphing!

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