Explain the vertex formula, Mathematics

Assignment Help:

Explain the Vertex Formula ?

The vertex formula is a convenient way of finding the vertex of the graph for any quadratic function. The graph of the quadratic equation f(x) = ax2 + bx + c has its vertex at:

(-b/2a, f(-b/2a))

In other words the x coordinate of the vertex is always x = -b/2a, which is also the equation for the axis of symmetry.

Symmetry
Note: this formula is derived from the standard form by completing the square.
Here's an example that you can look at:

Question: Use the vertex formula to find the vertex of the graph of the following function:
f(x) = -x 2 + 6x - 5

Solutions: Find the x-coordinate of the vertex first, using the vertex formula.
x = -b /2a
X = -6 / 2(-1)
X = -6/-2
X =3
This tells us that the vertex is the point (3, ?). We now need to find the y-coordinate, or functional value, for
x = 3.
f(3) = -(3) 2 + 6(3) - 5
= -9 + 18 -5
= 4
So, the vertex point of f(x) = -x2 +6x - 5 is the point (3,4)


Related Discussions:- Explain the vertex formula

Cone - three dimensional spaces, Cone - Three dimensional spaces The be...

Cone - Three dimensional spaces The below equation is the general equation of a cone. X 2 / a 2 + y 2 /b 2 = z 2 /c 2 Here is a diagram of a typical cone. Not

Three whole divisions, In the National Hockey championship, there are 30 in...

In the National Hockey championship, there are 30 independent ice hockey teams. Every of the teams will play 82 official NHL games every year. Many teams will have to travel from t

Kara brought $23 with her when she went shopping, Kara brought $23 with her...

Kara brought $23 with her when she went shopping. She spent $3.27 for lunch and $14.98 on a shirt. How much money does she have left? The two items that Kara bought must be sub

Geometry, how do you find the length of a parallel line connecting two exte...

how do you find the length of a parallel line connecting two external circles of different sizes from the outside, given the value of both radius and one parallel line.

Ordinary and partial differential equations, A differential equation is ter...

A differential equation is termed as an ordinary differential equation, abbreviated through odes, if this has ordinary derivatives in it. Similarly, a differential equation is term

Definition of logarithms, Q. Definition of Logarithms? Ans. A loga...

Q. Definition of Logarithms? Ans. A logarithm to the base a of a number x is the power to which a is raised to get x. In equation format: If x = a y , then log a  x

Differential equatoin, how to solve questions based on higher differential ...

how to solve questions based on higher differential equations

Multiplication and division, you want to share 34 pencils among 6 friends ....

you want to share 34 pencils among 6 friends .How many would each friend get?

Items price list, what is the unit price of 6.5 cups of pizza sauce?

what is the unit price of 6.5 cups of pizza sauce?

Arc Length and Sector Area, how do i find the diameter of a circle if i hav...

how do i find the diameter of a circle if i have the shaded sectors area of 263.76 and the central angle of that circle is 210 degrees?

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd