Answer:
We have axis of symmetry in [tex]x=-1[/tex]
The vertex point is [tex](-1, -9)[/tex]
The roots by factoring are
[tex]x=-4[/tex]
[tex]x=2[/tex]
Step-by-step explanation:
We have the function:
[tex]f(x)=x^2+2x-8[/tex]
Factoring the quadratic equation:
[tex]y=(x+4)(x-2)[/tex]
When [tex]y=0[/tex]
[tex]0=(x+4)(x-2)[/tex]
[tex]x=-4[/tex]
[tex]x=2[/tex]
The vertex point is [tex](h, k)[/tex]
From the equation, we have [tex]a=1,\:b=2 \text{ and }\:c=-8[/tex]
[tex]$h=-\frac{b}{2a}$[/tex]
[tex]$h=-\frac{2}{2\cdot \:1}$[/tex]
[tex]h=-1[/tex]
We also got the axis of symmetry
In order to find [tex]k[/tex] just use the [tex]$h=x_{vetex}$[/tex]:
[tex]k=(-1)^2+2(-1)-8\\k=1-2-8\\k=-9[/tex]
Once [tex]a>0[/tex], we have the minimum at [tex](-1, -9)[/tex]
Answer:
x = -1 axis of symmetry
(-1,-9) vertex
x = -4 x=2 are the roots
Step-by-step explanation:
y = x^2 + 2x - 8
The axis of symmetry is
h = -b/2a
h = -2/ (2*1) = -2/2 =-1
x = -1
The x coordinate of the vertex is at the axis of symmetry
To find the y value substitute into the function
y = (-1)^2 +2(-1) -8
y = 1-2-8
y = -9
The vertex is at ( -1,-9)
Factor
What 2 number multiply to -8 and add to 2
4*-2 = -8
4+-2 = 2
y = ( x+4) (x-2)
Using the zero product property to find the roots
0 = ( x+4) (x-2)
x+4 =0 x-2 =0
x = -4 x=2 are the roots
