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)+8 Answer:

Find the coordinates of the vertex of the following parabola algebraically. Write your answer as an (x,y) (x, y) point.\newliney=x2+8 y=x^{2}+8 \newlineAnswer:

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Precalculusright chevron icon
Complex conjugate theoremright 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+8 y=x^{2}+8 \newlineAnswer:
  1. Identify Equation Parameters: To find the vertex of a parabola in the form y=ax2+bx+cy = ax^2 + bx + c, we can use the vertex formula x=−b2ax = -\frac{b}{2a}. In this case, the equation is y=x2+8y = x^2 + 8, which means a=1a = 1 and b=0b = 0.
  2. Calculate x-coordinate: Since b=0b = 0, the formula simplifies to x=−0/(2⋅1)=0x = -0/(2\cdot1) = 0. This gives us the xx-coordinate of the vertex.
  3. Substitute xx into Equation: To find the yy-coordinate of the vertex, we substitute the xx-coordinate back into the original equation. So we substitute x=0x = 0 into y=x2+8y = x^2 + 8.
  4. Calculate y-coordinate: Substituting x=0x = 0 gives us y=(0)2+8=0+8=8y = (0)^2 + 8 = 0 + 8 = 8. This is the y-coordinate of the vertex.
  5. Find Vertex: Combining the xx and yy coordinates, we get the vertex of the parabola as (0,8)(0, 8).

More problems from Complex conjugate theorem

Question
Find the degree of this polynomial.\newline`5b^{10} + 3b^3`\newline_______
Get tutor helpright-arrow

Posted 5 months ago

Question
Subtract.\newline(9a+5)−(2a+4)(9a + 5) - (2a + 4)\newline____
Get tutor helpright-arrow

Posted 5 months ago

Question
Find the product. Simplify your answer. \newline−3v2(v2−9)-3v^2(v^2 - 9)\newline________
Get tutor helpright-arrow

Posted 5 months ago

Question
Find the product. Simplify your answer.\newline(v−3)(4v+1)(v - 3)(4v + 1)\newline______
Get tutor helpright-arrow

Posted 5 months ago

Question
Find the square. Simplify your answer.\newline(3y+2)2(3y + 2)^2\newline______
Get tutor helpright-arrow

Posted 5 months ago

Question
Divide. If there is a remainder, include it as a simplified fraction.\newline(24t2+36t)÷6t(24t^2 + 36t) \div 6t\newline______
Get tutor helpright-arrow

Posted 5 months ago

Question
Is the function q(x)=x6−9 q(x) = x^6 - 9 even, odd, or neither?\newlineChoices:\newline[[even][odd][neither]]\text{[[even][odd][neither]]}
Get tutor helpright-arrow

Posted 9 months ago

Question
Find the product. Simplify your answer. \newline−3q2(−3q2+q)-3q^2(-3q^2 + q)\newline______
Get tutor helpright-arrow

Posted 9 months ago

Question
Find the product. Simplify your answer.\newline(r+3)(4r+2)(r + 3)(4r + 2)\newline______
Get tutor helpright-arrow

Posted 9 months ago

Question
Find the roots of the factored polynomial.\newline(x+7)(x+4)(x + 7)(x + 4)\newlineWrite your answer as a list of values separated by commas.\newlinex=x = ____
Get tutor helpright-arrow

Posted 9 months ago

View all (33)

Related topics

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