![y = -\frac{1}{9}(x - 1)^2 - 6](https://tex.z-dn.net/?f=y%20%3D%20-%5Cfrac%7B1%7D%7B9%7D%28x%20-%201%29%5E2%20-%206)
Step-by-step explanation:
The vertex form of the equation for a parabola is given by
![y = a(x - h)^2 + k](https://tex.z-dn.net/?f=y%20%3D%20a%28x%20-%20h%29%5E2%20%2B%20k)
where (h, k) are the coordinates of the parabola's vertex. Since the vertex is at (1, -6), we can write the equation as
![y = a(x - 1)^2 - 6](https://tex.z-dn.net/?f=y%20%3D%20a%28x%20-%201%29%5E2%20-%206)
Also, since the parabola passes through (4, -7), we can use this to find the value for a:
![-7 = a(4 - 1)^2 - 6 \Rightarrow -7 = 9a - 6](https://tex.z-dn.net/?f=-7%20%3D%20a%284%20-%201%29%5E2%20-%206%20%5CRightarrow%20-7%20%3D%209a%20-%206)
or
![a = -\frac{1}{9}](https://tex.z-dn.net/?f=a%20%3D%20-%5Cfrac%7B1%7D%7B9%7D)
Therefore, the equation of the parabola is
![y = -\frac{1}{9}(x - 1)^2 - 6](https://tex.z-dn.net/?f=y%20%3D%20-%5Cfrac%7B1%7D%7B9%7D%28x%20-%201%29%5E2%20-%206)
Answer:
![\huge{ \fbox{ \sf{13 \: units}}}](https://tex.z-dn.net/?f=%20%5Chuge%7B%20%5Cfbox%7B%20%5Csf%7B13%20%5C%3A%20units%7D%7D%7D)
Option C is correct.
Step-by-step explanation:
![\star{ \sf{ \: Let \: the \: points \: be \: a \: and \: b}}](https://tex.z-dn.net/?f=%20%5Cstar%7B%20%5Csf%7B%20%5C%3A%20Let%20%5C%3A%20the%20%5C%3A%20points%20%5C%3A%20be%20%5C%3A%20a%20%5C%3A%20and%20%5C%3A%20b%7D%7D)
![\star{ \sf{ \: let \: A(-3, 2) \: be \: (x1 \:, y1) \: and \: B(9, -3) \: be \: (x2 \:, y2) }}](https://tex.z-dn.net/?f=%20%5Cstar%7B%20%5Csf%7B%20%5C%3A%20let%20%5C%3A%20A%28-3%2C%202%29%20%5C%3A%20be%20%5C%3A%20%28x1%20%5C%3A%2C%20y1%29%20%5C%3A%20%20and%20%20%5C%3A%20B%289%2C%20-3%29%20%5C%3A%20be%20%5C%3A%20%28x2%20%5C%3A%2C%20y2%29%20%7D%7D)
![\underline{ \sf{Finding \: the \: distance \: between \: the \: given \: points}} :](https://tex.z-dn.net/?f=%20%5Cunderline%7B%20%5Csf%7BFinding%20%5C%3A%20the%20%5C%3A%20distance%20%5C%3A%20between%20%5C%3A%20the%20%5C%3A%20given%20%5C%3A%20points%7D%7D%20%3A%20)
![\boxed{ \sf{Distance = \sqrt{ {(x2 - x1)}^{2} + {(y2 - y1)}^{2} } }}](https://tex.z-dn.net/?f=%20%5Cboxed%7B%20%5Csf%7BDistance%20%3D%20%20%5Csqrt%7B%20%7B%28x2%20-%20x1%29%7D%5E%7B2%7D%20%20%2B%20%20%7B%28y2%20-%20y1%29%7D%5E%7B2%7D%20%7D%20%7D%7D)
![\mapsto{ \sf{ \sqrt{ {(9 - ( - 3))}^{2} + {( - 3 - 2)}^{2} } }}](https://tex.z-dn.net/?f=%20%5Cmapsto%7B%20%5Csf%7B%20%20%5Csqrt%7B%20%7B%289%20-%20%28%20-%203%29%29%7D%5E%7B2%7D%20%2B%20%20%7B%28%20-%203%20-%202%29%7D%5E%7B2%7D%20%20%7D%20%7D%7D)
![\mapsto{ \sf{ \sqrt{ {(9 + 3)}^{2} + {( - 3 - 2)}^{2} }}}](https://tex.z-dn.net/?f=%20%5Cmapsto%7B%20%5Csf%7B%20%5Csqrt%7B%20%7B%289%20%2B%203%29%7D%5E%7B2%7D%20%20%2B%20%20%7B%28%20-%203%20-%202%29%7D%5E%7B2%7D%20%7D%7D%7D)
![\mapsto{ \sf{ \sqrt{ {(12)}^{2} + {( - 5)}^{2} } }}](https://tex.z-dn.net/?f=%20%5Cmapsto%7B%20%5Csf%7B%20%5Csqrt%7B%20%7B%2812%29%7D%5E%7B2%7D%20%20%2B%20%20%7B%28%20-%205%29%7D%5E%7B2%7D%20%7D%20%7D%7D)
![\mapsto{ \sf{ \sqrt{144 + 25}}}](https://tex.z-dn.net/?f=%20%5Cmapsto%7B%20%5Csf%7B%20%5Csqrt%7B144%20%2B%2025%7D%7D%7D%20)
![\mapsto{ \sf{ \sqrt{169} }}](https://tex.z-dn.net/?f=%20%5Cmapsto%7B%20%5Csf%7B%20%5Csqrt%7B169%7D%20%7D%7D)
![\mapsto{ \sf{ \sqrt{ {(13)}^{2} } }}](https://tex.z-dn.net/?f=%20%5Cmapsto%7B%20%5Csf%7B%20%5Csqrt%7B%20%7B%2813%29%7D%5E%7B2%7D%20%7D%20%7D%7D)
![\mapsto{ \sf{ 13 \: units}}](https://tex.z-dn.net/?f=%20%5Cmapsto%7B%20%5Csf%7B%2013%20%5C%3A%20units%7D%7D)
Hope I helped!
Best regards! :D
~![\text{TheAnimeGirl}](https://tex.z-dn.net/?f=%20%5Ctext%7BTheAnimeGirl%7D)
Y= 6x + 1.
6x represents six times, and the +1 is “one more.”
Answer:
1
Step-by-step explanation:
The amplitude is the maximum distance away from the middle of the wave. Here we can see that the middle of the wave is the x axis and the farthest point (largest difference between the y coordinate of the x-axis, or the line y = 0, and the wave) is 1 unit away.
Answer:
1. The right triangles pass the AA similarity congruence theorem.
2. s/q
Step-by-step explanation:
They are similar since they pass the AA( Angle-Angle) similarity theorem.
Similar triangles have corresponding proportional sides so side z corresponds with side s and side x corresponds with q so we would represent that as
s/q