Rewrite the function in standard form, intercept form, find the vertex, find the y-intercept, and find the x-intercepts. show your work y=(x+4)^2-1

Standard form - y=x^{2}+8x+15

Intercept form - y=(x+5)(x+3)

The vertex is  is (-4,-1)

y intercept=(0,15)

X intercepts (-5,0) and (-3,0)

Step-by-step explanation:

The given quadratic equation is

and we know that the standard form of the quadratic equation is

so on comparing with it the above is the standard form only and also we can get the value of a (coefficient of ) and b( coefficient of x) and constant c so we get them as follows

a=1, b=8 c= 15 now ac=16 so the two numbers whose product is 15 and add is 8 are 5,3

so writing the equation in the Intercept form is

now lets find the vertex,now recall that all parabolas are symmetrical. This means that the axis of symmetry is halfway between the x−intercepts or their average.

axis of symmetry

This is also the x−coordinate of the vertex. To find the y−coordinate, plug the x−value into either form of the quadratic equation. We will use Intercept form.

so, the vertex is (-4,-1).

now Vertex form is written as , where (h,k) is the vertex and a is the same as in the other two forms.

for Y intercept put x=0 in the given vertex form

y=

y intercept=(0,15)

for X intercept put y=0 in intercept form

X intercepts (-5,0) and (-3,0)

sine

step-by-step explanation:

6 adults and 9 children went.

a + c = 15

12a + 9c = 153

12(6) + 9(9) = 153

72 + 81 = 153