Hi there!
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⇒ Graph : [tex]y=6x^2+1[/tex]
∴ Rewrite the equation in vertex form.
⇒ [tex]y = 6 ( x + 0)^2 + 1[/tex]
∴ Use the vertex form, [tex]y = a(x - h)^2 + k[/tex] , to determine the values of [tex]a , h ,[/tex] and [tex]k[/tex]
[tex]a = 6 \\h = 0\\k = 1[/tex]
∴ Since the value of [tex]a[/tex] is positive, the parabola opens up.
⇵
∴ Find the vertex [tex]( h,k)[/tex].
[tex](0,1)[/tex]
∴ Find [tex]p[/tex], the distance from the vertex to the focus.
[tex]\frac{1}{24}[/tex]
∴ Find the focus.
[tex]( 0 , \frac{25}{24} )[/tex]
∴ Find the axis of symmetry by finding the line that passes through the vertex and the focus.
[tex]x = 0[/tex]
∴ Find the directrix.
[tex]y = \frac{23}{24}[/tex]
∴ Use the properties of the parabola to analyze and graph the parabola.
Direction: Opens Up
⇒ Vertex: [tex]( 0 , 1)[/tex]
⇒ Focus: [tex]( 0 , \frac{25}{24} )[/tex]
⇒ Axis of Symmetry: [tex]x = 0[/tex]
⇒ Directrix: [tex]y = \frac{23}{24}[/tex]
∴ Select a few [tex]x[/tex] values, and plug them into the equation to find the corresponding [tex]y[/tex] values. The [tex]x[/tex] values should be selected around the vertex.
[tex]x : -2 , -1 , 0 , 1 , 2 \\y : 25 , 7 , 1 , 7 , 25[/tex]
Hope this helped you!
