how to find vertex of quadratic function
HOW TO FIND VERTEX OF A QUADRATIC FUNCTION
How to Find Vertex of a Quadratic Function :
Here we are going to see some example problems to understand finding vertex of a quadratic function.
How to Find Vertex of a Quadratic Function ?
To find the vertex form of the parabola, we use the concept completing the square method.
Vertex form of a quadratic function :
y = a(x - h)2 + k
In order to find the maximum or minimum value of quadratic function, we have to convert the given quadratic equation in the above form.
To find vertex using completing the square method, please visit the page"How to Find the Minimum or Maximum Value of a Function in Vertex Form"
Finding Vertex of a Quadratic Function - Examples
Question 1 :
Find the vertex of the graph of the given function f.
f(x) = 7x2 − 12
Solution :
We may write the given equation as,
f(x) = 7(x - 0)2 − 12
y = a(x - h)2 + k
By comparing the above equation with vertex form, we get
Vertex (h, k) ==> (0, -12)
(ii) f(x) = −9x2 − 5
Solution :
We may write the given equation as,
f(x) =−9(x - 0) 2 − 5
y = a(x - h)2 + k
By comparing the above equation with vertex form, we get
Vertex (h, k) ==> (0, -5)
(iii) f(x) = (x − 2)2 − 3
Solution :
We may write the given equation as,
f(x) =(x − 2) 2 − 3
y = a(x - h)2 + k
By comparing the above equation with vertex form, we get
Vertex (h, k) ==> (2, -3)
(iv) f(x) = (x + 3)2 + 4
Solution :
We may write the given equation as,
f(x) = (x + 3) 2 + 4
y = a(x - h)2 + k
By comparing the above equation with vertex form, we get
Vertex (h, k) ==> (-3, 4)
(v) f(x) = (2x − 5)2 + 6
Solution :
We may write the given equation as,
f(x) = (2x − 5) 2 + 6
f(x) = 4x2 - 2(2x) (5) + 52 + 6
f(x) = 4x2 - 20x + 25 + 6
f(x) = 4x2 - 20x + 31
f(x) = 4[x2 - 5x] + 31
f(x) = 4[x2 - 2 ⋅x ⋅(5/2) + (5/2)2 - (5/2)2 ] + 31
f(x) = 4[x + (5/2)]2 - 4(25/4) + 31
f(x) = 4[x + (5/2)]2 + 6
y = a(x - h)2 + k
By comparing the above equation with vertex form, we get
Vertex (h, k) ==> (-5/2, 6)
(vi) f(x) = (7x + 3)2 + 5
Solution :
We may write the given equation as,
f(x) = (7x + 3) 2 + 5
= 72 (x + (3/7))2 + 5
= 49 (x + (3/7))2 + 5
y = a(x - h)2 + k
By comparing the above equation with vertex form, we get
Vertex (h, k) ==> (-3/7, 5)
After having gone through the stuff given above, we hope that the students would have understood " How to Find Vertex of a Quadratic Function".
Apart from the stuff given in this section, if you need any other stuff in math, please use our google custom search here.
If you have any feedback about our math content, please mail us :
v4formath@gmail.com
We always appreciate your feedback.
You can also visit the following web pages on different stuff in math.
WORD PROBLEMS
HCF and LCM word problems
Word problems on simple equations
Word problems on linear equations
Word problems on quadratic 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
how to find vertex of quadratic function
Source: https://www.onlinemath4all.com/how-to-find-vertex-of-a-quadratic-function.html
Posted by: rodriguenother44.blogspot.com
0 Response to "how to find vertex of quadratic function"
Post a Comment