画出 $y = 5 - (x - 2)^2$ 的函数图像，并清晰地标出顶点和 y 轴截距。 利用你的图像，解释为什么 $5 - (x - 2)^2 = 7$ 无解。 答案 （作答与解题空间）

1. Identify the turning point and shape of the graph

$y=5-(x-2)^2=-(x-2)^2+5$
This is in the form $y=-(x-p)^2+q$, so the turning point is $(p,q)=(2,5)$.

Since the coefficient of $(x-2)^2$ is negative, the parabola opens downwards.

2. Find the y-intercept

At the y-intercept, $x=0$.

$y=5-(0-2)^2$
$y=5-4=1$

So the y-intercept is $(0,1)$.

3. Complete the sketch with labels

Draw a smooth parabola opening downwards, with maximum point labelled $(2,5)$ and crossing the y-axis at $(0,1)$. The graph is symmetric about $x=2$.

1. Compare the required value $y=7$ with the maximum value of the graph

From the graph, the turning point is $(2,5)$ and the parabola opens downwards, so the maximum value of $y$ is $5$.

Since $7>5$, the horizontal line $y=7$ does not meet the graph of $y=5-(x-2)^2$.