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Multiple Choice
Determine if the parabola opens up or down.
A
Up
B
Down
C
To the left
D
To the right
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1
Identify the general form of a quadratic equation, which is \(y = ax^2 + bx + c\), where \(a\), \(b\), and \(c\) are constants.
Determine the key features of the quadratic graph: the vertex, axis of symmetry, direction of opening (upward if \(a > 0\), downward if \(a < 0\)), and the y-intercept.
Find the vertex using the formula for the x-coordinate: \(x = -\frac{b}{2a}\). Then substitute this value back into the equation to find the corresponding y-coordinate.
Plot the vertex and y-intercept on the coordinate plane. Use symmetry about the axis of symmetry to find additional points by choosing x-values on either side of the vertex and calculating their y-values.
Draw a smooth curve through the plotted points to complete the graph of the quadratic equation, ensuring it opens in the correct direction based on the sign of \(a\).