![Added by Tony B]()
The given problem is already in the vertex form.
color(blue)"The vertex form"The vertex form
color(maroon)(y=a(x-h)^2+k)y=a(x−h)2+k
Where (h,k)(h,k) is the vertex.
Our problem
y=-2(x+1)^2+7y=−2(x+1)2+7
y=-2(x-(-1))^2+7y=−2(x−(−1))2+7
(h,k) = (-1,7)(h,k)=(−1,7)
The vertex is (-1,7)(−1,7)
Intercepts on xx and yy axes occur where the curve crosses them.
To find yy intercept we need to plug in x=0x=0
y=-2(0+1)^2+7y=−2(0+1)2+7
y=-2(1)+7y=−2(1)+7
y=-2+7y=−2+7
y=5y=5
The y-y−intercept is (0,5)(0,5)
For finding x-x−intercepts, we need to plug in y=0y=0
0=-2(x+1)^2+70=−2(x+1)2+7
Subtract 77 from both ends and isolating the term containing xx
-7 = -2(x+1)^2−7=−2(x+1)2
Let us rewrite it as -2(x+1)^2=-7−2(x+1)2=−7 It looks better to when the variable is kept of the left side of the equation.
-2(x+1)^2=-7−2(x+1)2=−7 dividing by -2−2 on both sides isolates (x+1)^2(x+1)2
We get
(x+1)^2=7/2(x+1)2=72
Take square root on both the sides we get
sqrt((x+1)^2) = +-sqrt(7/2)√(x+1)2=±√72
x+1 = +-sqrt(7/2)x+1=±√72
Subtract 11 from both sides to solve for xx
x=-1+-sqrt(7/2)x=−1±√72
The x-x−intercepts are (-1+sqrt(7/2))(−1+√72) and (-1-sqrt(7/2))(−1−√72)
