what is the solution set for x^2-8x+4-3? x7 71 x1 or x

Question

what is the solution set for x^2-8x+4>-3? x<1 or x>7 71 x>1 or x<7 7

hero · Answer

x^2 - 8x + 4 > - 3

Add 3 to both sides:
x^2 - 8x + 4 + 3 > 0
x^2 - 8x + 7 > 0

hero · Answer

The left side factors to
(x - 7)(x - 1) > 0

Find the value of the vertex
$$\left(-\frac{b}{2a}, f(-\frac{b}{2a})\right)$$

Then graph x^2 - 8x + 7

hero · Answer

From there, you can easily observe the parts where the graph is greater than zero

anonymous · Answer

Thank you ( : does this work for all problems like this?

anonymous · Answer

what is the variable f? @Hero

hero · Answer

For this set of problems, yes.

hero · Answer

We can refer to the quadratic as f(x) = x^2 - 8x - 7

hero · Answer

Once you find the x coordinate of the vertex, you substitute it in for x, then evaluate

hero · Answer

Have you found the x coordinate for the vertex yet?