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:

What is the focus of the parabola y=−8x2+1y= -8x^2+1? Simplify any fractions.

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Algebra 2right chevron icon
Find the focus or directrix of a parabolaright chevron icon

Full solution

Q. What is the focus of the parabola y=−8x2+1y= -8x^2+1? Simplify any fractions.
  1. Identify Parabola Form: Identify the form of the parabola and its orientation.\newlineGiven equation: y=−8x2+1y = -8x^2 + 1.\newlineThis is a vertical parabola since it's in the form y=ax2+ky = ax^2 + k.
  2. Convert to Vertex Form: Convert the equation to vertex form and identify aa, hh, and kk. The equation y=−8x2+1y = -8x^2 + 1 is already in the form y=a(x−h)2+ky = a(x - h)^2 + k where a=−8a = -8, h=0h = 0, and k=1k = 1.
  3. Calculate Value of p: Calculate the value of p using the formula p=14ap = \frac{1}{4a}.\newlineSubstitute a=−8a = -8 into p=14ap = \frac{1}{4a}.\newlinep=14(−8)=1−32=−132p = \frac{1}{4(-8)} = \frac{1}{-32} = -\frac{1}{32}.
  4. Determine Focus: Determine the focus of the parabola using the vertex (h,k)(h, k) and the value of pp. The vertex is (0,1)(0, 1). Since the parabola opens downwards (a < 0), the focus is at (0,k+p)(0, k + p). Focus = (0,1−132)=(0,3132)(0, 1 - \frac{1}{32}) = (0, \frac{31}{32}).

More problems from Find the focus or directrix 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 (53)

Related topics

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