5
-3
The vertex of this parabola is at -2 -3 When the y-value is -2 the x-value is -5. The coefficient of the squared term in the parabola's equation is -3.
2
A parabola with vertex (h, k) has equation of the form: y = a(x - h)² + k → vertex (k, h) = (-2, -3), and a point on it is (-1, -5) → -5 = a(-1 - -2)² + -3 → -5 = a(1)² - 3 → -5 = a - 3 → a = -2 → The coefficient of the x² term is -2.
5
The coordinates will be at the point of the turn the parabola which is its vertex.
-3
-5
-3
9
The vertex of this parabola is at 5 5 When the x-value is 6 the y-value is -1. The coefficient of the squared expression in the parabola's equation is -6.
y = -5 By using calculus, the derivative of y = -2.5(x-4)2 - 5 is y' = -5(x-4). Solving the equation -5(x-4) = 0 gives x = 4 (since the slope of the parabola at the vertex is zero). Plug this back into the equation: y = -2.5(4 - 4) -5 = -5, so the y-coordinate is -5. The equation of the parabola is given in the vertex form y = a(x - h)2 + k, where (h, k) is the vertex. So the vertex is (4, -5).
The vertex of this parabola is at -2 -3 When the y-value is -2 the x-value is -5. The coefficient of the squared term in the parabola's equation is -3.
The vertex of this parabola is at -5 -2 When the x-value is -4 the y-value is 2. The coefficient of the squared expression in the parabola's equation is 4. y = a(x - h)2 + k; (h, k) = (-5, -2); (x, y) = (-4, 2) 2 = a[-4 -(-5)]2 - 2, add 2 to both sides 4 = a(-4 +5)2 4 = a(1)2 4 = a
So you need something like this: y = a*(x - 4)² + 3. This will make the vertex be at (4,3). Then it looks like you have another point on the parabola (3,5). Plug that in and solve for a. 5 = a*(3-4)² + 3. This becomes 5 = a + 3, so a=2, then the equation is: y = 2*(x - 4)² + 3
2