Solving systems of equations graphically

Question

$$y=(x-2)^2+4$$

$$2x+y=7$$

I'm not quite sure how I would graph these. Just a line or parabola? And how would I tell?

Would I expand the first equation or use $2$ and $4$ to get the points?

Any pointers are greatly appreciated.

Answer 1

1) Draw the parabola (the first equation). Reduce to canonical form, you'll find that the minimum is reached at point $(2,4)$. It crosses $y$-axis at $(0,8)$.

2) Draw line (the second equation). It crosses $y$-axis at $(0,7)$ and $x$-axis at $\left(\frac72,0\right)$.

3) Find their intersection point(s):

Answer 2

Draw the parabola $y=(x-2)^2+4$ and the line $y=-2x+7$ and find common points.

Answer 3

prove that $y=-2x+7$ is a Tangent line to the given parabola

Answer 4

In simple cases the solution can be clearly seen. Like in this plot, the lines have one common point at $(1,5)$, which is also easy to check.