Question

7. The curve y = (x + 2)² has a minimum point at?

8. The coordinates of the lowest point on the curve: y = x² - 4x + 1 are?

Answer 1

7. If branches of a parabola a directed upwards and it has roots $a$ and $b$, then the parabola has minimum point at $x =\frac{a+b}{2}$. $y=(x+2)^2$ is a parabola with repeated root $-2$, which means it has minimum at $-2$.

8. For a parabola $y=ax^2+bx+c$ we can use equation $x_m=-\frac{b}{2a}$ for x coordinate of minimum point. Parabola $y = x^2 - 4x + 1$ has minimum point at $x_m=-\frac{-4}{2*1}=2$ and it's y coordinate is $y_m=2^2-4*2+1=-3$ . So, the minimum point is $(2,-3)$