# How do you graph y= (x-4)^2 +3 ?

Aug 24, 2015

Determine the vertex and several points, preferably on mirror images of the parabola. Plot points and sketch a curve through the points. Do not connect the dots.

#### Explanation:

$y = {\left(x - 4\right)}^{2} + 3$

The equation is in vertex form, $y = a {\left(x - h\right)}^{2} = k$, where $\left(h , k\right)$ is the vertex, and $a = 1$, $h = 4$, and $k = 3$. The vertex $\left(h , k\right) = \left(4 , 3\right)$.

Determine several points on the parabola, substituting both positive and negative numbers for $x$, and making sure to get points on both sides of the parabola. A mirror image is preferred. $y = {\left(x - 4\right)}^{2} + 3$

$x = 0 ,$ $y = 19$
$x = 1 ,$ $y = 12$
$x = 2 ,$ $y = 7$
$x = 6 ,$ $y = 7$
$x = 7 ,$ $y = 12$
$x = 8 ,$ $y = 19$

Plot the vertex and the points that you determined. Sketch a parabola (curve) through the points with the vertex as the minimum point. Do not connect the dots.

graph{y=(x-4)^2+3 [-15.09, 16.93, -1.09, 14.93]}