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Use the quadratic function to determine the sign of the leading coefficient, vertex, and the equation of the axis of symmetry

User Webdeb
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Step 1:

Write the quadratic function


ax^2\text{ + bx + c = 0}

Step 2:

The graph of a quadratic function is a curve called a parabola. Parabolas may open upward or downward and vary in "width" or "steepness", but they all have the same basic "U" shape.

Step 3:


\text{For ax}^2\text{ + bx + c = 0}

The leading coefficient 'a' is positive, so it opens upwards.


For-ax^2\text{ + bx + c = 0}

The leading coefficient is '-a' positive, so it opens downwards.

Step 4:

Vertex


\begin{gathered} \text{The x coordinate of the vertex is x = }(-b)/(2a) \\ Next,\text{ substitute the x into the equation to find the y coordinate.} \end{gathered}

Step 5:

Equation of the axis of symmetry

Parabolas also have an axis of symmetry, which is parallel to the y-axis. The axis of symmetry is a vertical line drawn through the vertex.


\text{The axis of symmetry of this }parabola\text{ will be a line x = }(-b)/(2a)

User Kccqzy
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