How do you find the focus, directrix and sketch #y=1/3x^2x#?
Focus
Vertex
directrix: y=
Make sure you can picture your graph as a concave up graph. A concave down graph will have a negative sign included
Now, all you have to do is to graph your equation just make sure you know your xintercepts and yintercepts ie xintercepts is when y=0 and yintercepts is when x=0 so your xintercepts are (0,0) AND (3,0) and your yintercept is (0,0) graph{y = 1/3x^2x [10, 10, 5, 5]}
By signing up, you agree to our Terms of Service and Privacy Policy
To find the focus and directrix of the parabola represented by the equation ( y = \frac{1}{3}x^2  x ), you can use the standard form of a parabolic equation ( y = ax^2 + bx + c ). Then, use the formulas for finding the focus and directrix of a parabola in this form.

Identify the coefficients of ( x^2 ), ( x ), and the constant term.
 ( a = \frac{1}{3} )
 ( b = 1 )
 ( c = 0 )

Use the formula for finding the focus of a parabola: ( F = \left( \frac{b}{2a}, \frac{1}{4a} \right) ).

Use the formula for finding the equation of the directrix: ( y = \frac{1}{4a} ).

Substitute the values of ( a ) and ( b ) into the formulas to find the focus and directrix.

Sketch the parabola, focusing on the vertex, focus, and directrix.
Using these steps:
 ( a = \frac{1}{3} ), ( b = 1 )
 Focus ( F = \left( \frac{(1)}{2(\frac{1}{3})}, \frac{1}{4(\frac{1}{3})} \right) = \left( \frac{3}{2}, \frac{3}{2} \right) )
 Directrix ( y = \frac{1}{4(\frac{1}{3})} = \frac{3}{4} )
 Focus: ( F = \left( \frac{3}{2}, \frac{3}{2} \right) ), Directrix: ( y = \frac{3}{4} )
 Sketch the parabola, emphasizing the vertex at the origin, the focus, and the directrix.
Therefore, the focus of the parabola is ( \left( \frac{3}{2}, \frac{3}{2} \right) ) and the equation of the directrix is ( y = \frac{3}{4} ).
By signing up, you agree to our Terms of Service and Privacy Policy
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
 How do you identify the vertex, focus, directrix and the length of the latus rectum and graph #y=x^212x+20#?
 How do you write the standard Form of the parabola equation given Vertex (3 , 3) Focus (3 , 9/4)?
 What is a quadratic function with a maximum at #(3, 125)# and roots at #2# and #8#?
 How do I find all the critical points of #f(x)=x^2+4x2#?
 What are the conic sections of the following equations #4x ^2 + 4y ^2  60=0#?
 98% accuracy study help
 Covers math, physics, chemistry, biology, and more
 Stepbystep, indepth guides
 Readily available 24/7