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How do you find the vertex of the parabola y equals -4x2 - 16x - 11?
Wiki User
∙ 13y ago
You would convert it to vertex form by completing the square. You can also find the optimum value as optimum value and vertex are the same.
Wiki User
∙ 13y ago
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How to find vertex of y equals 4x to the power of 2 plus 16x?
y = 4x² + 16x ; Take the derivative: y' = 8x + 16. Set equal to zero, and x = -2. Substitute into the original: y = 4(-2)² + 16*(-2) = -16, so the vertex is (-2,16). Or, factor to y = 4x(x + 4). The zeros of this are x = 0 and x = -4. Since a parabola is symmetric, the vertex is halfway between these, or x = -2, then substitute as above and get (-2,16).
What is the x in 16x equals 4?
.25
How many solutions are in the set 16x plus 2 - 8 equals 16x plus 24?
16x + 2 - 8 = 16x + 24 implies 16x - 6 = 16x + 24 subtracting 16x from both sides, this implies: -6 = 24 So the equation has no soultions.
How do you solve 8x2 plus 16x plus 8 equals 0?
8x2 + 16x + 8 = 0
16x to the 4th power - 1 equals?
1
What is the vertex of the parabola of y equals -4x 2-16x-11?
f(x) = -4x2 - 16x - 11 a = -4, b = -16, c = -11 x-coordinate of the vertex = -b/2a = -(-16)/2(-4) = 16/-8 = -2 y-coordinate = f(-2) = -4(-2)2 -16(-2) - 11 = -16 + 32 - 11 = 5 vertex is (-2, 5)
How to find vertex of y equals 4x to the power of 2 plus 16x?
y = 4x² + 16x ; Take the derivative: y' = 8x + 16. Set equal to zero, and x = -2. Substitute into the original: y = 4(-2)² + 16*(-2) = -16, so the vertex is (-2,16). Or, factor to y = 4x(x + 4). The zeros of this are x = 0 and x = -4. Since a parabola is symmetric, the vertex is halfway between these, or x = -2, then substitute as above and get (-2,16).
What is the x in 16x equals 4?
.25
How many solutions are in the set 16x plus 2 - 8 equals 16x plus 24?
16x + 2 - 8 = 16x + 24 implies 16x - 6 = 16x + 24 subtracting 16x from both sides, this implies: -6 = 24 So the equation has no soultions.
Find the vertex of the parabola y -4x2 - 16x - 11?
Start by finding the x-coordinate of that vertex. You can do that by taking the derivative of the function and solving for zero: y = -4x2 - 16x - 11 y' = -8x - 16 0 = -8x - 16 8x = -16 x = -2 Now simply plug the x-coordinate into the original equation to get your y-coordinate: y = -4(-2)2 - 16(-2) - 11 y = -16 + 32 - 11 y = 5 So the vertex occurs at the point (-2, 5) Alternative answer: It should be noted that the above method requires a little extra work if you are not working with a parabola, as the first derivative only allows you to find the critical points of a function. With an arbitrary function, you also need to take the second derivative of the function to determine if the critical point is a maximum, minimum or point of inflection. If you don't know Calculus yet, there is also an algebraic method to find the vertex of a parabola We have: y = -4x^2 - 16x - 11 This is the parabola's standard form. In order to find the vertex through algebra we need to convert it to vertex form: y = a(x - h) + k Where (h,k) is our vertex We can do this by factoring (which is always a pain): First factor out a -4: y = -4(x^2 + 4x) - 11 We left the -11 alone because 11/4 is pretty ugly to work with, so we will leave it on the side for now. Next we complete the square: y = -4(x^2 + 4x + c - c) - 11 y = -4(x^2 + 4x + c) - 11 + 4c We want to find c, such that 2*(c^(1/2)) = 4, which gives us c = 4. y = -4(x^2 + 4x + 4) - 11 + 16 y = -4(x + 2)^2 + 5 Comparing with our vertex form: y = a(x - h) + k We have a = -4, h = -2 and k = 5. (h, k) is our vertex, which gives us (-2, 5). This is consistent with the answer given by the Calculus method above, which is reassuring.
How do you solve 8x2 plus 16x plus 8 equals 0?
8x2 + 16x + 8 = 0
16x to the 4th power - 1 equals?
1
What is the slope of any line parallel to 16x-2y equals 4?
16X - 2Y = 4- 2Y = - 16X + 4Y = 8X - 2---------------m(slope) = 8===========
What is x in 16x-15-6x equals 13?
If: 16x-15-6x = 13 Then: 10x = 28 And: x = 2.8.
What property is 16x plus 5y equals 5y plus 16x?
The Commutative Property of Addition.
What is 16x divided by 100 equals 3564.28?
16x/100 = 3564.28 Multiply both sides by 100: 16x = 356428 Divide both sides by 16: x = 22276.75
What is x in 16x plus 10 equals 131?
7.5625
