posted by zachary on .
Given the following quadratic equation, find;?
a. the vertex
b. the axis of symmetry
c. the intercepts
d. the domain
e. the range
f. the interval where the function is increasing, and
g. the interval where the function is decreasing
h. Graph the function. y= -x^2+2x+8
Which quadratic equation? y=-x^2+2x+8?
x = -b/2a gives you the x-value of the vertex. find y by subsituting into the original equation.
axis of symmetry uses the information found above.
Factor your equation and set = to zero to find the intercepts Is there a negative sign in front of the x^2 term. You have it originally, but it is missing in what you typed again.
The domain is all real numbers. This is true any time you have this type of function. We only have to worry about limiting the domain when we have fractions or roots.
You can find your range with the help of the vertex which is a turning point. The y-values will all be greater than or less than the y at the turning point depending on the direction of your graph. I can't help here because I don't know if there is a negative sign in front of the x^2 or not. Remember the range is the y - values.
If you have a u-shaped graph facing up.
It will decrease to the vertex and then increase to the right of the vertex.
If you have a u-shaped graph facing down or upside-down. It will increase to the vertex and then decrease to the right of the vertex.
To graph, use the vertex, the two intercepts. you might try to add another point her two based on that sketch.