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 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 3

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 4

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 5

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 6

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 7

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 8

Draw the graph of $y=-(x+1)(x+2)$.

\( \begin{align} \displaystyle
-(x+1)(x+2) & = 0 \\
x+1 &= 0 \text{ or } x+2 = 0 \\
\therefore x &= -1 \text{ or } x = -2 \\
\end{align} \)





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