Vertex Form and Parabola Transformations

$h$ represents the x-value of the vertex, which makes the expression inside the brackets equal to zero. This value shifts the parabola horizontally along the x-axis.

$k$ represents the y-value of the vertex, which determines the vertical shift of the parabola.

The vertex of the equation $y=-3(x-4{)}^2+7$ is at $(4,7)$. The term $(x-4)$ shows that $h=4$, and the number outside the brackets, 7, represents $k$.

The vertex of the equation $y=2(x+3{)}^2-5$ is at $(-3,-5)$. The term $(x+3)$ is equivalent to $(x-(-3))$, so $h=-3$, and $k=-5$.

The vertex of the equation $y=-4(x-1{)}^2+6$ is at $(1,6)$. The term $(x-1)$ shows that $h=1$, and the number outside the brackets, 6, represents $k$.

Since the coefficient of $a$ is negative, the parabola opens downward, making the vertex the highest point. The term $(x+5)$ indicates that $h=-5$, and the number outside the brackets, -2, represents $k$. Therefore, the highest point is at $(-5,-2)$.