Trigonometry Examples

Find the Axis of Symmetry y=-3x^2+6x+5
Rewrite the equation in vertex form.
Tap for more steps...
Complete the square for .
Tap for more steps...
Use the form , to find the values of , , and .
Consider the vertex form of a parabola.
Substitute the values of and into the formula .
Simplify the right side.
Tap for more steps...
Cancel the common factor of and .
Tap for more steps...
Factor out of .
Cancel the common factors.
Tap for more steps...
Factor out of .
Cancel the common factor.
Rewrite the expression.
Cancel the common factor of and .
Tap for more steps...
Factor out of .
Move the negative one from the denominator of .
Multiply by .
Find the value of using the formula .
Tap for more steps...
Simplify each term.
Tap for more steps...
Raise to the power of .
Multiply by .
Divide by .
Multiply by .
Add and .
Substitute the values of , , and into the vertex form .
Set equal to the new right side.
Use the vertex form, , to determine the values of , , and .
Since the value of is negative, the parabola opens down.
Opens Down
Find the vertex .
Find , the distance from the vertex to the focus.
Tap for more steps...
Find the distance from the vertex to a focus of the parabola by using the following formula.
Substitute the value of into the formula.
Simplify.
Tap for more steps...
Multiply by .
Move the negative in front of the fraction.
Find the focus.
Tap for more steps...
The focus of a parabola can be found by adding to the y-coordinate if the parabola opens up or down.
Substitute the known values of , , and into the formula and simplify.
Find the axis of symmetry by finding the line that passes through the vertex and the focus.
Cookies & Privacy
This website uses cookies to ensure you get the best experience on our website.
More Information