# Math

13. Find the vertex of the parabola.
y = -2x2 + 12x - 13
(5, -3)
(-3, 5)
(3, 5)
(5, 3)

1. 👍 0
2. 👎 0
3. 👁 188
1. y = -2x^2 + 12x - 13
there are many ways to determine the vertex, but the easiest (for me) i think is to use derivatives. first we get the derivative with respect to x:
y = -2x^2 + 12x - 13
y' = -4x + 12
then we equate this to zero (because vertex is a maximum or a minimum and therefore the slope is zero):
0 = -4x + 12
4x = 12
x = 3
substitute this back to the original given equation:
y = -2x^2 + 12x - 13
y = -2(3^2) + 12(3) - 13
y = -18 + 36 - 13
y = 5
therefore vertex is at
(3, 5)

hope this helps~ :)

1. 👍 0
2. 👎 1
2. As always, love your comrentamy on the world around us.I do have a quick rationale for why the bold 'Contains peanuts', though.It's somewhere at the intersection of allergies and the covering our buttness of most companies.Anything that can be potentially allergy-inducing (peanuts, soy, wheat, milk, and I am sure that list will only get longer) seems to now be showing up in bold at the bottom of ingredient lists. On one hand this is a good thing for those parents who need to scan each label attached to the foods they buy for allergic kids. Sometimes the lists are akin to Russian literature and this saves time (though most parents I know read the list anyways, so this part of the rationale is somewhat moot). On the other hand, this is a way for companies to ward off litigious consumers. Remember the somewhere close to 3 million (that's dollars!) reasons McDonald's paper coffee cups have 'warning, contents are hot' signs on them?And that pretty much gets us back to your original theory - do we really have a hope to teach advanced learning theories to a society that doesn't recognize that coffee is hot and peanuts contain peanuts? Or could it be that people do know this but will do pretty much anything to make a buck?

1. 👍 0
2. 👎 0

## Similar Questions

1. ### Algebra

An engineer designs a satellite dish with a parabolic cross section. The dish is 10 ft wide at the​ opening, and the focus is placed 8 ft from the vertex. ​a) Position a coordinate system with the origin at the vertex and

2. ### Algebra

Please help.! 1) Given the following three points, find by hand the quadratic function they represent. (0,6), (2,16), (3, 33) A. f(x)=4x2−3x+6 B. f(x)=4x2+3x+6 C. f(x)=−4x2−3x+6 D. f(x)=−4x2+21x+6 2) Given the following

3. ### Algebra 2

1.) The cost in C dollars of manufacturing x bicycles at Holliday's Production Plant is given by the function C(x) = 2x2 - 800x + 92,000. Find the minimum cost. 2.) The vertex of y = -3x2- 6x - 9 lies in which quadrant? 3.) Given

4. ### Algebra

An engineer designs a satellite dish with a parabolic cross section. The dish is 14 ft wide at the​ opening, and the focus is placed 4 ft from the vertex. ​a) Position a coordinate system with the origin at the vertex and

1. ### Calculus

Find expressions for the quadratic functions whose graphs are shown. One graph has the point (4,2) plotted in which the parabola passes through (U-shaped parabola- right side up) The vertex is at (3,0) and the parabola does not

2. ### Math

Which expression is the expanded form of p(x)=4(x−7)(2x2+3)? 8x3−56x2+12x−84 8x3+56x2−12x−84 32x3−224x2+48x−336 −48x2+12x−84 I believe it is 8x3−56x2+12x−84 if I am wrong can you explain

3. ### Algebra

The reflecting dish of a parabolic microphone has a cross-section in the shape of a parabola. The microphone itself is placed on the focus of the parabola. If the parabola is 60 inches wide and 30 inches deep, how far from the

4. ### Algebra 2

The equation of a parabola is 12y=(x-1)^2-48. Identify the vertex, focus, and directrix of the parabola.

1. ### pre cal

What is the center of the conic whose equation is x^2 + 2y^2 - 6x + 8y = 0 2.Which one of the following equations represents a hyperbola? (5 points) A) 3x^2 + y^2 + 12x - 7 = 0 B) 3x^2 + 3y^2 + 12x - 7 = 0 C) 3x^2 + y + 12x - 7 =

2. ### math

A parabola passes through the point (3, 5) on its way to the vertex at (7, 11). Determine the equation in vertex form that represents this parabola.

3. ### Algebra

Consider the graph of the equation y=ax^2+bx+c, when a does not equal 0. If a is multiplied by 3, what is true of the graph of the resulting parabola? (A) The Vertex is 3 units above the vertex of the original. (B) The new

4. ### Precalculus

Find the vertex, focus, and axis of symmetry of the parabola x^2-10x-8y+29 = 0. ==> I do it over and over and over, but I keep getting the same answers of (5,4) for the vertex, (5,6) for the focus, and x = 5 for the LOS, but