Answer:
[tex]-\frac{1}{2}x^2-5x-8[/tex]
Step-by-step explanation:
Since the graph passes through both (-8,0) and (-2,0), the vertex's x value must be the average of the two, or -5. To determine the y value, you need the third point, (-6,4). In a parabola without any dilation or stretching, the difference between the y value of the point 1 unit to the side of the vertex and the point 3 units away is 9-1=8. However, here it is 4, meaning that this graph has a dilation of 1/2. This means that the vertex has a y value of 9/2=4.5, and that the vertex is (-5,4.5). From here, you can simply plug in the known values to get the vertex form, and then convert to standard. [tex]y=-\dfrac{1}{2}(x+5)^2+4.5[/tex], which in standard form is [tex]-\dfrac{1}{2}\cdot (x+5)(x+5)+4.5=-\dfrac{1}{2}x^2-5x-8[/tex]. Hope this helps!
