To find the equation of the parabola in standard form, we can use the general equation of a parabola, which is y = ax^2 + bx + c.
We can substitute the coordinates of the given points into this equation to form a system of equations.
When x = 0, y = 1:
1 = a(0)^2 + b(0) + c
1 = 0 + 0 + c
c = 1
When x = 1, y = -3:
-3 = a(1)^2 + b(1) + 1
-3 = a + b + 1
When x = -1, y = -9:
-9 = a(-1)^2 + b(-1) + 1
-9 = a - b + 1
Now, we have a system of equations:
1 = c
-3 = a + b + 1
-9 = a - b + 1
From the first equation, we know that c = 1. We can substitute this value into the second and third equations:
-3 = a + b + 1
-9 = a - b + 1
Rearranging these equations, we get:
a + b = -4
a - b = -10
To solve this system of equations, we can add the two equations together:
(a + b) + (a - b) = -4 + (-10)
2a = -14
a = -7
Substituting this value back into one of the equations, we can solve for b:
-7 + b = -10
b = -10 + 7
b = -3
Therefore, the equation of the parabola in standard form is:
y = -7x^2 - 3x + 1
Write the equation, in standard form, of the parabola containing the following points: (0, 1), (1, -3), (-1, -9).
You must set up a system of three equations in your work in order to get full credit for this question.
(1 point)
Responses
y=3x2−5x−1
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=
3
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2
−
5
�
−
1
y is equal to 3 x squared minus 5 x minus 1
y=−x2+5x+3
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=
−
�
2
+
5
�
+
3
y is equal to negative x squared plus 5 x plus 3
y=−7x2+3x+1
�
=
−
7
�
2
+
3
�
+
1
y is equal to negative 7 x squared plus 3 x plus 1
y=−3x2+7x+1
1 answer
1 answer