If a quadratic has a vertex at (-2,2) and passes through (-1,0) what is its equation in standard form?
A. y = -2(x-2)^2 + 2
B. y = -2(x+2)^2 + 2
C. y = -(x+2)^2 - 2
D. y = (x+2)^2 + 2
Is the answer B?
of course, B
To determine the equation of a quadratic in standard form, we need to use the vertex form of a quadratic equation. The vertex form of a quadratic equation is given by:
y = a(x - h)^2 + k,
where (h, k) represents the vertex of the parabola.
In this case, we are given that the vertex is (-2, 2). So, h = -2 and k = 2. Plugging these values into the vertex form equation, we get:
y = a(x - (-2))^2 + 2
= a(x + 2)^2 + 2
Now, we know that the quadratic passes through the point (-1, 0). To find the value of 'a', we can substitute these coordinates into the equation:
0 = a((-1) + 2)^2 + 2
= a(1)^2 + 2
= a + 2
Subtracting 2 from both sides of the equation, we have:
a = -2
Finally, substituting this value of 'a' back into the equation, we get:
y = -2(x + 2)^2 + 2
Comparing this equation to the answer choices, we can see that the correct answer is option B: y = -2(x + 2)^2 + 2.
Therefore, the answer is B.