Consider the graphs of a quadratic function and a linear function on the same set of axes. cutting2 points of intersection $b^2-4ac \gt 0$ touching1 point of intersection $b^2-4ac = 0$ missingno points of intersection $b^2-4ac \lt 0$ In the graphs meet, the coordinates of the points of intersection of the graphs can be found [...]

# Parabola Graph in Intercept Form $y=a(x-b)(x-c)$
$$y=a(x-b)(x-c)$$ Concave up for $a \gt 0$ Concave down for $a \lt 0$ Example 1 Draw the graph of $y=(x-1)(x+2)$. \begin{align} \displaystyle (x-1)(x+2) & = 0 \\ x-1 &= 0 \text{ or } x+2 = 0 \\ \therefore x &= 1 \text{ or } x = -2 \\ \end{align} Example 2 Draw the [...]
# Quadratic Graph of $y=(x-a)^2$ Completed Square Form
$$y=(x-a)^2+b$$ Example 1 Draw the graph of $y=(x-1)^2+2$. The vertex is $(1,2)$ and the graph is concave up. Example 2 Draw the graph of $y=(x-1)^2-2$. The vertex is $(1,-2)$ and the graph is concave up. Example 3 Draw the graph of $y=(x+1)^2+2$. The vertex is $(-1,2)$ and the graph is concave up. Example 4 Draw [...]