Resourcesdown chevron
Testimonials
Plans
Sign in
Sign up
Resourcesright arrow
Testimonials
Plans
Bytelearn - cat image with glassesAI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Find the coordinates of the vertex of the following parabola algebraically. Write your answer as an (x,y) point. y=-x^(2)-16 x-57 Answer:

Find the coordinates of the vertex of the following parabola algebraically. Write your answer as an (x,y) (x, y) point.\newliney=−x2−16x−57 y=-x^{2}-16 x-57 \newlineAnswer:

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Algebra 2right chevron icon
Find the axis of symmetry of a parabolaright chevron icon

Full solution

Q. Find the coordinates of the vertex of the following parabola algebraically. Write your answer as an (x,y) (x, y) point.\newliney=−x2−16x−57 y=-x^{2}-16 x-57 \newlineAnswer:
  1. Factor out x terms: The vertex form of a parabola's equation is y=a(x−h)2+ky = a(x - h)^2 + k, where (h,k)(h, k) is the vertex of the parabola. To find the vertex of the parabola given by y=−x2−16x−57y = -x^2 - 16x - 57, we need to complete the square to rewrite the equation in vertex form.
  2. Complete the square: First, we factor out the coefficient of the x2x^2 term from the xx terms. Since the coefficient is −1-1, we have:\newliney=−1(x2+16x)−57y = -1(x^2 + 16x) - 57
  3. Rewrite the equation: Next, we find the value that completes the square for the expression x2+16xx^2 + 16x. This value is (16/2)2=64(16/2)^2 = 64. We add and subtract this value inside the parentheses to complete the square:\newliney=−1(x2+16x+64−64)−57y = -1(x^2 + 16x + 64 - 64) - 57
  4. Distribute and simplify: Now we rewrite the equation, grouping the terms that create a perfect square trinomial and combining the constants: y=−1((x+8)2−64)−57y = -1((x + 8)^2 - 64) - 57
  5. Final vertex form: Distribute the −1-1 and simplify the constants:\newliney=−(x+8)2+64−57y = -(x + 8)^2 + 64 - 57\newliney=−(x+8)2+7y = -(x + 8)^2 + 7
  6. Final vertex form: Distribute the −1-1 and simplify the constants:\newliney=−(x+8)2+64−57y = -(x + 8)^2 + 64 - 57\newliney=−(x+8)2+7y = -(x + 8)^2 + 7Now the equation is in vertex form, y=a(x−h)2+ky = a(x - h)^2 + k, where a=−1a = -1, h=−8h = -8, and k=7k = 7. Therefore, the vertex of the parabola is (h,k)=(−8,7)(h, k) = (-8, 7).

More problems from Find the axis of symmetry of a parabola

Question
What is the focus of the parabola y=−x2y = -x^2?\newlineSimplify any fractions.\newline(_____ , _____)\newline
Get tutor helpright-arrow

Posted 8 months ago

Question
The equation of a parabola is y=x2−10x+25y = x^2 - 10x + 25. Write the equation in vertex form.\newlineWrite any numbers as integers or simplified proper or improper fractions.\newline______
Get tutor helpright-arrow

Posted 8 months ago

Question
In which direction does the parabola x+y2=−7x + y^2 = -7 open?\newlineChoices:\newline(A) up\text{up}\newline(B) down\text{down}\newline(C) right\text{right}\newline(D) left\text{left}
Get tutor helpright-arrow

Posted 9 months ago

Question
What is the vertex of the parabola y=−4(x−2)2+2y = -4(x - 2)^2 + 2??\newline(_,_)(\_,\_)
Get tutor helpright-arrow

Posted 9 months ago

Question
What is the axis of symmetry of the parabola x=12(y+3)2+5x = \frac{1}{2}(y + 3)^2 + 5?
Get tutor helpright-arrow

Posted 9 months ago

Question
In which direction does the parabola x−2y2=−5x - 2y^2 = -5 open?\newlineChoices:\newline[A]up\text{[A]up}\newline[B]down\text{[B]down}\newline[C]right\text{[C]right}\newline[D]left\text{[D]left}
Get tutor helpright-arrow

Posted 9 months ago

Question
What is the vertex of the parabola y−8x2=4y - 8x^2 = 4? \newline(_,_)(\_,\_)
Get tutor helpright-arrow

Posted 7 months ago

Question
The equation of a circle is x2+(y+4)2=1 x^{2}+(y+4)^{2}=1 . What are the center and radius of the circle?\newlineChoose 11 answer:\newline(A) The center is (−4,0) (-4,0) and the radius is 11 .\newline(B) The center is (4,0) (4,0) and the radius is 11 .\newline(C) The center is (0,4) (0,4) and the radius is 11 .\newline(D) The center is (0,−4) (0,-4) and the radius is 11 .
Get tutor helpright-arrow

Posted 10 months ago

Question
y=(x−3)(x+9) y=(x-3)(x+9) \newlineThe given equation is graphed in the xy x y -plane. Which of the following are x x -intercepts of the graph?\newlineChoose 11 answer:\newline(A) −3-3 and −9-9\newline(B) −3-3 and 99\newline(C) 33 and −9-9\newline(D) 33 and 99
Get tutor helpright-arrow

Posted 10 months ago

Question
If y=2x2−5x+7 y=2 x^{2}-5 x+7 is graphed in the xy x y -plane, which of the following characteristics of the graph is displayed as a constant or coefficient in the equation?\newlineChoose 11 answer:\newline(A) x x -intercept(s)\newline(B) y y -intercept\newline(C) x x -coordinate of the vertex\newline(D) y y -coordinate of the vertex
Get tutor helpright-arrow

Posted 10 months ago

View all (19)

Related topics

Algebra - Order of OperationsAlgebra - Distributive Property`X` and `Y` AxesGeometry - Scalene TriangleCommon MultipleGeometry - Quadrant