Graphing Quadratic Functions (Solutions)
- The vertex of the parabola \(y=x^2\) is (0, 0). This makes sense because when \(x=0\), then \(y=0^2\), and then \(y=0\)
- The parent parabola \(y=x^2\) opens up.
- For a parabola written in standard form, when \(a = 0\), the result is a line. This makes sense because if the squared term is zero, then the result is a linear equation.
- When \(a > 0\), the graph opens up. When \(a < 0\), the graph opens down. When \(|a| > 1\), the shape of the graph is stretched (wider). When \(|a| \) is between 0 and 1, then the shape of the graph is compressed (narrower). Changing \(b \) moves the location of the parabola in an arch around the original vertex, but it does not change the shape. Changing \(c \) moves the location of the parabola up or down, but it does not change the shape.
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