SOLUTION: write the function f(x)=4x^2-48x-141 in vertex form, and identify its vertex

Question 391299: write the function f(x)=4x^2-48x-141 in vertex form, and identify its vertex

Answer by haileytucki(390) (Show Source): You can put this solution on YOUR website!
f(x)=4x^(2)-48x-141
Replace f(x) with y to find the properties of the parabola.
y=4x^(2)-48x-141
To create a trinomial square on the left-hand side of the equation, add a value to both sides of the equation that is equal to the square of half the coefficient of x. In this problem, add (-6)^(2) to both sides of the equation.
y=4(x^(2)-12x+36)+4(-(141)/(4))-(4)(0+36)
Remove the 0 from the polynomial; adding or subtracting 0 does not change the value of the expression.
y=4(x^(2)-12x+36)+4(-(141)/(4))-(4)(36)
Factor the perfect trinomial square into (x-6)^(2).
y=4((x-6)^(2))+4(-(141)/(4))-(4)(36)
Factor the perfect trinomial square into (x-6)^(2).
y=4(x-6)^(2)+4(-(141)/(4))-(4)(36)
Multiply 4 by each term inside the parentheses.
y=4(x-6)^(2)-141-(4)(36)
Multiply 4 by 36 to get 144.
y=4(x-6)^(2)-141-(144)
Multiply -1 by the 144 inside the parentheses.
y=4(x-6)^(2)-141-144
Subtract 144 from -141 to get -285.
y=4(x-6)^(2)-285
This is the form of a paraboloa. Use this form to determine the values used to find vertex and x-y intercepts.
y=a(x-h)^(2)+k
Use the standard form to determine the vertex and x-y intercepts.
a=4_k=-285_h=6
The vertex of a parabola is (h,k).
Vertex: (6,-285)
RELATED QUESTIONS
Write the function f(x)=-5x^2-60x-181 in vertex form, and identify its... (answered by josgarithmetic,ikleyn)

Write the function f(x) = -5x2 - 60x - 181 in vertex form, and identify its... (answered by Fombitz)

need help write the function f(x)=-5xSquared -60x-181 in vertex form and identify its... (answered by ewatrrr)

Write f(x)=-5x^2-60x-181 in vertex form and identify the... (answered by stanbon)

Please help I don't understand. Question: write each function in vertex form and... (answered by lynnlo)

Write in vertex form. Sketch a graph of the function and label its vertex. 1. y = x^2 + (answered by Fombitz)

Identify the vertex: 1.) f(x)=-(x-3)^2+2 2.) f(x)= 2(x+9)^2-4 Write each function in... (answered by Fombitz)

Write the quadratic function in standard form. Identify the vertex, axis of symmetry, and (answered by Fombitz)

Write the quadratic function in vertex form and then find the vertex: y=x^2+4x+7... (answered by Alan3354)