Question

Please help! Thank you!

Answer 1

y = -½x² - 5x - 8

Explanation:

y = a(x - b)(x - c)

y = a(x - -8)(x - -2)

y = a(x + 8)(x + 2)

Using (-6,4)

4 = a(-6 + 8)(-6 + 2)

4 = a(2)(-4)

a = 4/-8

a = -½

y = -½(x² + 10x + 16)

y = -½x² - 5x - 8

Answer 2

`-(1)/(2)x^2-5x-8`

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.
`y=-(1)/(2)(x+5)^2+4.5`, which in standard form is
`-(1)/(2)\cdot (x+5)(x+5)+4.5=-(1)/(2)x^2-5x-8`. Hope this helps!