Solve y=3x^2-12x 17

Function

Find the vertex

Find the axis of symmetry

Rewrite in vertex form

(34, - 3468)

Show Solution

Testing for symmetry about the origin

Testing for symmetry about the x-axis

Testing for symmetry about the y-axis

Not symmetry with respect to the origin

Show Solution

Find the standard equation of the parabola

Find the vertex of the parabola

Find the focus of the parabola

(x - 34)^{2} = \frac{1}{3} (y + 3468)

Show Solution

Solve for x

Solve for y

x = \frac{102 + 10404 + 3 y}{3} x = \frac{102 - 10404 + 3 y}{3}

Evaluate

y = 3 x^{2} - 12 x \times 17

Simplify

y = 3 x^{2} - 204 x

Swap the sides of the equation

3 x^{2} - 204 x = y

Move the expression to the left side

3 x^{2} - 204 x - y = 0

Substitute a= 3,b= - 204 and c= - y into the quadratic formula x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

x = \frac{204 \pm ( - 204 ) ^{2} - 4 \times 3 ( - y )}{2 \times 3}

Simplify the expression

x = \frac{204 \pm ( - 204 ) ^{2} - 4 \times 3 ( - y )}{6}

Simplify the expression

More Steps

x = \frac{204 \pm 41616 + 12 y}{6}

Simplify the radical expression

More Steps

x = \frac{204 \pm 2 10404 + 3 y}{6}

Separate the equation into 2 possible cases

x = \frac{204 + 2 10404 + 3 y}{6} x = \frac{204 - 2 10404 + 3 y}{6}

Simplify the expression

More Steps

x = \frac{102 + 10404 + 3 y}{3} x = \frac{204 - 2 10404 + 3 y}{6}

Solution

More Steps

x = \frac{102 + 10404 + 3 y}{3} x = \frac{102 - 10404 + 3 y}{3}

Show Solution

r = 0 r = \frac{sin ( θ ) + 204 cos ( θ )}{3 cos ^{2} ( θ )}

Show Solution