Answer

Verified

350.1k+ views

**Hint**: To simplify this question , we need to solve it step by step . In order to solve and write the find the vertex of a quadratic equation . We will use the vertex formula and determine the y- coordinate of the vertex of a parabola in simplest form by using the formula $ \left( { - \dfrac{b}{{2a}},f(x)} \right) $ . We will first determine the x-coordinate and then we fill substitute the found x-coordinate in the quadratic equation to determine y-coordinate of the vertex of a parabola with the following equation $ y = {x^2} - 8x + 18 $

We can also use the quadratic in vertex form method to get our required result.

**:**

__Complete step-by-step answer__A quadratic equation is written as $ a{x^2} + bx + c $ in its standard form . As we know that in the quadratic equation , a is the coefficient of the first term in the quadratic, b is the coefficient of the second term and c is the coefficient of the third term in the quadratic.

Now we are Assessing the coefficients of our quadratic equation given $ y = {x^2} - 8x + 18 $

The values of a, b and c are as follows =.

$

a = 1 \\

b = - 8 \\

c = 18 \;

$

And the vertex can be found by using the formula $ \left( { - \dfrac{b}{{2a}}} \right) $

Vertex = $ \left( { - \dfrac{b}{{2a}},f(x)} \right) $

Now , we will substitute the values in this formula we get

$

\left( { - \dfrac{b}{{2a}}} \right) \\

\Rightarrow - \dfrac{{( - 8)}}{{2 \times 1}} \\

\Rightarrow \dfrac{8}{2} \\

\Rightarrow 4 \;

$

This 4 is the required x-coordinate of the vertex of parabola .

Now , looking at the formula of Vertex $ \left( { - \dfrac{b}{{2a}},f(x)} \right) $ , we got x- coordinate . We will be substituting the x-coordinate into the given quadratic equation $ y = {x^2} - 8x + 18 $ to get the required y-coordinate of the vertex of the parabola

By Substituting , we get-

Vertex = $ \left( { - \dfrac{b}{{2a}},f(x)} \right) $

This formula becomes and when simplifying further , we will get vertex .

Vertex = $ (4,2) $

Therefore , $ (4,2) $ is the required vertex and 2 is the required y-coordinate of the vertex of the parabola with the quadratic equation $ y = {x^2} - 8x + 18 $ .

**Note**: If \[a > 0\], the parabola opens upward. If \[a < 0\] , the parabola opens downward.

The general form of a parabola to find the equation for the axis of symmetry.

The axis of symmetry is defined by $ x = \left( { - \dfrac{b}{{2a}}} \right) $ .

The vertex of a parabola will be either a maximum or a minimum, the range will consist of all y-values greater than or equal to the y-coordinate of the vertex or less than or equal to the y-coordinate at the turning point, depending on whether the parabola opens up or down.

Always try to understand the mathematical statement carefully and keep things distinct .

Recently Updated Pages

How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE

Why Are Noble Gases NonReactive class 11 chemistry CBSE

Let X and Y be the sets of all positive divisors of class 11 maths CBSE

Let x and y be 2 real numbers which satisfy the equations class 11 maths CBSE

Let x 4log 2sqrt 9k 1 + 7 and y dfrac132log 2sqrt5 class 11 maths CBSE

Let x22ax+b20 and x22bx+a20 be two equations Then the class 11 maths CBSE

Trending doubts

Guru Purnima speech in English in 100 words class 7 english CBSE

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Which are the Top 10 Largest Countries of the World?

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths

Difference Between Plant Cell and Animal Cell

Change the following sentences into negative and interrogative class 10 english CBSE

Select the word that is correctly spelled a Twelveth class 10 english CBSE

Give 10 examples for herbs , shrubs , climbers , creepers