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Find the Solutions to X 2 18 Brainly

Graphing Quadratic Equations Using the Axis of Symmetry

A quadratic equation is a polynomial equation of degree 2 .  The standard form of a quadratic equation is

0 = a x 2 + b x + c

where a , b and c are all real numbers and a 0 .

If we replace 0 with y , then we get a quadratic function

y = a x 2 + b x + c

whose graph will be a parabola .

The axis of symmetry of this parabola will be the line x = b 2 a . The axis of symmetry passes through the vertex, and therefore the x -coordinate of the vertex is b 2 a . Substitute x = b 2 a in the equation to find the y -coordinate of the vertex. Substitute few more x -values in the equation to get the corresponding y -values and plot the points. Join them and extend the parabola.

Example 1:

Graph the parabola y = x 2 7 x + 2 .

Compare the equation with y = a x 2 + b x + c to find the values of a , b , and c .

Here, a = 1 , b = 7 and c = 2 .

Use the values of the coefficients to write the equation of axis of symmetry .

The graph of a quadratic equation in the form y = a x 2 + b x + c has as its axis of symmetry the line x = b 2 a . So, the equation of the axis of symmetry of the given parabola is x = ( 7 ) 2 ( 1 ) or x = 7 2 .

Substitute x = 7 2 in the equation to find the y -coordinate of the vertex.

y = ( 7 2 ) 2 7 ( 7 2 ) + 2 = 49 4 49 2 + 2 = 49 98 + 8 4 = 41 4

Therefore, the coordinates of the vertex are ( 7 2 , 41 4 ) .

Now, substitute a few more x -values in the equation to get the corresponding y -values.

x y = x 2 7 x + 2
0 2
1 4
2 8
3 10
5 8
7 2

Plot the points and join them to get the parabola.

Example 2:

Graph the parabola y = 2 x 2 + 5 x 1 .

Compare the equation with y = a x 2 + b x + c to find the values of a , b , and c .

Here, a = 2 , b = 5 and c = 1 .

Use the values of the coefficients to write the equation of axis of symmetry.

The graph of a quadratic equation in the form y = a x 2 + b x + c has as its axis of symmetry the line x = b 2 a . So, the equation of the axis of symmetry of the given parabola is x = ( 5 ) 2 ( 2 ) or x = 5 4 .

Substitute x = 5 4 in the equation to find the y -coordinate of the vertex.

y = 2 ( 5 4 ) 2 + 5 ( 5 4 ) 1 = 50 16 + 25 4 1 = 50 + 100 16 16 = 34 16 = 17 8

Therefore, the coordinates of the vertex are ( 5 4 , 17 8 ) .

Now, substitute a few more x -values in the equation to get the corresponding y -values.

x y = 2 x 2 + 5 x 1
1 8
0 1
1 2
2 1
3 4

Plot the points and join them to get the parabola.

Example 3:

Graph the parabola x = y 2 + 4 y + 2 .

Here, x is a function of y . The parabola opens "sideways" and the axis of symmetry of the parabola is horizontal. The standard form of equation of a horizontal parabola is x = a y 2 + b y + c where a , b , and c are all real numbers and a 0 and the equation of the axis of symmetry is y = b 2 a .

Compare the equation with x = a y 2 + b y + c to find the values of a , b , and c .

Here, a = 1 , b = 4 and c = 2 .

Use the values of the coefficients to write the equation of axis of symmetry.

The graph of a quadratic equation in the form x = a y 2 + b y + c has as its axis of symmetry the line y = b 2 a . So, the equation of the axis of symmetry of the given parabola is y = 4 2 ( 1 ) or y = 2 .

Substitute y = 2 in the equation to find the x -coordinate of the vertex.

x = ( 2 ) 2 + 4 ( 2 ) + 2 = 4 8 + 2 = 2

Therefore, the coordinates of the vertex are ( 2 , 2 ) .

Now, substitute a few more y -values in the equation to get the corresponding x -values.

y x = y 2 + 4 y + 2
5 7
4 2
3 1
1 1
0 2
1 7

Plot the points and join them to get the parabola.

Find the Solutions to X 2 18 Brainly

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