Given the expression of the quadratic function
Finding the symmetry point of the function
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Given the expression of the quadratic function
Finding the symmetry point of the function
To solve this problem, we'll find the vertex of the quadratic function .
Now, let's work through each step:
Step 1: The function given is . Here, and .
Step 2: Use the vertex formula . Substituting the values, we get .
Step 3: Substitute back into the function to find the y-coordinate: .
Therefore, the symmetry point of the function is .
Given the expression of the quadratic function
Finding the symmetry point of the function
\( f(x)=-5x^2+10 \)
The vertex formula is a shortcut derived from completing the square! It's faster and reduces calculation errors, especially when dealing with larger coefficients like -6 and 24.
That's perfectly fine! When c = 0 (like in our example), you still use the same vertex formula. The missing constant term doesn't affect finding the x-coordinate of the vertex.
Look at the coefficient of x². If a is negative (like -6), the parabola opens downward, so the vertex is a maximum. If a is positive, it's a minimum.
You could factor f(x) = -6x² + 24x = -6x(x - 4), but this gives you the x-intercepts (0 and 4), not the vertex. The vertex formula is more direct for finding the turning point.
The vertex shows the optimal point - like maximum profit, highest point of a ball's path, or minimum cost. Since our parabola opens down, (2, 24) represents the maximum value.
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