Given:
[tex]y=x^2[/tex]
Let's graph the parabola.
To graph the parabola, apply the vertex form of a parabola:
[tex]\begin{gathered} y=a(x-h)^2+k \\ \\ y=1(x-0)^2+0 \end{gathered}[/tex]
Thus, we have the values:
a = 1
h = 0
k = 0.
• The vertex is:
(h, k) ==> (0, 0)
• The parabola opens up since the value of ,a ,is positive.
Now, let's find more points using the equation.
• When x = 1
[tex]\begin{gathered} y=1^2 \\ y=1 \end{gathered}[/tex]
When x = -1:
[tex]\begin{gathered} y=-1^2 \\ y=1 \end{gathered}[/tex]
When x = 2:
[tex]\begin{gathered} y=2^2 \\ y=4 \end{gathered}[/tex]
When x = -2:
[tex]\begin{gathered} y=-2^2 \\ y=4 \end{gathered}[/tex]
When x = 3:
[tex]\begin{gathered} y=3^2 \\ y=9 \end{gathered}[/tex]
When x = -3:
[tex]\begin{gathered} y=-3^2 \\ y=9 \end{gathered}[/tex]
Therefore, we have the points:
(0, 0), (1, 1), (-1, 1), (2, 4), (-2, 4), (3, 9), (-3, 9)
Plot the points and connect them to form a parabola.
We have the graph below:
