Answer:
Step-by-step explanation:
y=x²+4x-7
=x²+4x+4-4-7
=(x+2)²-11
axis of symmetry is x=-2
vertex is (-2,-11)
x²+4x-7=0
[tex]x=\frac{-4 \pm\sqrt{4^2-4(1)(-7)} }{2(1)} \\=\frac{-4 \pm \sqrt{16+28} }{2} \\=\frac{-4 \pm 2\sqrt{11} }{2} \\=-2 \pm\sqrt{11}[/tex]
Answer:
Axis of symmetry is x = -2
(-2, -11) is the vertex
Roots are
-2 + [tex]\sqrt{11}[/tex], -2 - [tex]\sqrt{11}[/tex]
Step-by-step explanation:
a) Axis of symmetry equation is: x = -b/2a
Original equation: y = [tex]x^2+4x-7[/tex]
So...
x= -4/2(1) = -2
Axis of symmetry is x = -2
b) Vertex Point can be found by plugging into original equation.
[tex]y =x^2+4x-7[/tex]
=> y = [tex](-2)^2+4(-2)-7[/tex]
=> 4 - 8 - 7 = y
=> -11 = y
(-2, -11) is the vertex
c) quadratic formula is [tex]x = \frac{-b +-\sqrt{b^2-4ac} }{2a}[/tex]
Lets plug in the values.
[tex]\frac{-4 +- \sqrt{4^{2}-4(1)(-7) } }{2(1)}[/tex]
[tex]\frac{-4 +- \sqrt{16+28 } }{2}[/tex]
[tex]\frac{-4 +- \sqrt{44 } }{2}[/tex]
[tex]\sqrt{44} = 2\sqrt{11}[/tex]
-4 +- 2[tex]\sqrt{11}[/tex]
--------------
2
Here, i will factor out 2, and take out the +- and make it into two equations
2(-2 + [tex]\sqrt{11}[/tex]) / 2 = -2 + [tex]\sqrt{11}[/tex]
2(-2 - [tex]\sqrt{11}[/tex]) / 2 = -2 - [tex]\sqrt{11}[/tex]
x= -2 + [tex]\sqrt{11}[/tex]
or
x = -2 - [tex]\sqrt{11}[/tex]
Roots are
-2 + [tex]\sqrt{11}[/tex], -2 - [tex]\sqrt{11}[/tex]