# FIND THE VERTEX OF PARABOLA

How to find the vertex of parabola :

The vertex of a parabola is the point where the parabola crosses its axis of symmetry.

The vertex of the parabola is the highest or lowest point also known as maximum value or minimum value of the parabola.Here we are going to see how to find the vertex of the parabola.

If the parabola is open upward then vertex will be the lowest point

If the parabola is open downward then the vertex will be the highest point of the parabola.

The standard equation of the parabola is

y = ax² + bx + c

Vertex form of the parabola :

y = a (x - h)² + k

here (h, k) is known as vertex of the parabola.

To find the value of "h" we need to use the formula "-b/2a". By applying this x -coordinate in the given equation we will get the value of y that is "k".

Let us see some example problems to understand the method.

## Find the vertex of parabola - Examples

Example 1 :

Find the vertex of the parabola y = x² - 2 x - 5

Solution :

Method 1 :

Compare the given equation with the general form of quadratic equation

y = x² - 2 x - 5

y = ax² + b x + c

a =  1, b = -2 and c = -5

x - coordinate of vertex = -b/2a ==> - (-2)/2(1) ==> 1

Now we have t o apply x = 1 in the given equation according to get the value of y.

y = (1)² - 2(1) - 5

y = 1 - 2 - 5

y = 1 - 7  ==> -6

Vertex of the parabola is (1,6)

We can do the same problem in another method also.

Method 2 :

y = x² - 2 x - 5

Now we are going to convert the given equation in vertex form using completing the square method.

y = x² - 2 x(1) + 1² - 1² - 5

y = (x - 1) - 6

y = a (x - h)² + k

(h, k) ==> (1, 6)

Hence the vertex of the parabola is (1, 6).

Let us see the next example problem on "Find the vertex of parabola".

Example 2 :

Find the vertex of the parabola y = -x² - 14 x - 59

Solution :

Method 1 :

Compare the given equation with the general form of quadratic equation

y = -x² - 14 x - 59

y = ax² + b x + c

a =  -1, b = -14 and c = -59

x - coordinate of vertex = -b/2a ==> - (-14)/2(-1) ==> -7

Now we have t o apply x = 7 in the given equation according to get the value of y.

y = -(-7)² - 14(-7) - 59

y = -49 + 98 - 59

y = -108 + 98 ==> -10

Vertex of the parabola is (-7, -10)

We can do the same problem in another method also.

Method 2 :

y = -x² - 14 x - 59

y = -[x² + 14 x + 59]

Now we are going to convert the given equation in vertex form using completing the square method.

y = -[x² + 2 x(7) + 7² - 7² + 59]

y = -[(x + 7)² - 49 + 59]

y = -[(x + 7)² + 10]

y = a (x - h)² + k

(h, k) ==> (-7, -10)

Hence the vertex of the parabola is (-7, -10).

Let us see the next example problem on "Find the vertex of parabola".

Example 3 :

Find the vertex of the parabola y = x² + 4 x

Solution :

Method 1 :

Compare the given equation with the general form of quadratic equation

y = x² + 4 x

y = ax² + b x + c

a =  1, b = 4 and c = 0

x - coordinate of vertex = -b/2a ==> -4/2(1) ==> -2

Now we have t o apply x = -2 in the given equation according to get the value of y.

y = (-2)² + 4 (-2)

y = 4 - 8 ==> -4

Vertex of the parabola is (-2, -4)

We can do the same problem in another method also.

Method 2 :

y = x² + 4 x

Now we are going to convert the given equation in vertex form using completing the square method.

y = x² + 2 x(2) + 2² - 2²

y = (x + 2)² - 4

(h, k) ==> (-2, -4)

Hence the vertex of the parabola is (-2, -4).

After having gone through the stuff given above, we hope that the students would have understood "Find the vertex of parabola".

Apart from the stuff given in this section, if you need any other stuff in math, please use our google custom search here.

WORD PROBLEMS

HCF and LCM  word problems

Word problems on simple equations

Word problems on linear equations

Algebra word problems

Word problems on trains

Area and perimeter word problems

Word problems on direct variation and inverse variation

Word problems on unit price

Word problems on unit rate

Word problems on comparing rates

Converting customary units word problems

Converting metric units word problems

Word problems on simple interest

Word problems on compound interest

Word problems on types of angles

Complementary and supplementary angles word problems

Double facts word problems

Trigonometry word problems

Percentage word problems

Profit and loss word problems

Markup and markdown word problems

Decimal word problems

Word problems on fractions

Word problems on mixed fractrions

One step equation word problems

Linear inequalities word problems

Ratio and proportion word problems

Time and work word problems

Word problems on sets and venn diagrams

Word problems on ages

Pythagorean theorem word problems

Percent of a number word problems

Word problems on constant speed

Word problems on average speed

Word problems on sum of the angles of a triangle is 180 degree

OTHER TOPICS

Profit and loss shortcuts

Percentage shortcuts

Times table shortcuts

Time, speed and distance shortcuts

Ratio and proportion shortcuts

Domain and range of rational functions

Domain and range of rational functions with holes

Graphing rational functions

Graphing rational functions with holes

Converting repeating decimals in to fractions

Decimal representation of rational numbers

Finding square root using long division

L.C.M method to solve time and work problems

Translating the word problems in to algebraic expressions

Remainder when 2 power 256 is divided by 17

Remainder when 17 power 23 is divided by 16

Sum of all three digit numbers divisible by 6

Sum of all three digit numbers divisible by 7

Sum of all three digit numbers divisible by 8

Sum of all three digit numbers formed using 1, 3, 4

Sum of all three four digit numbers formed with non zero digits

Sum of all three four digit numbers formed using 0, 1, 2, 3

Sum of all three four digit numbers formed using 1, 2, 5, 6