Question

Find the turning point of y = x2 + 4x – 3 by completing the square

Answer 1

Answer:

(-2,7)

Step-by-step explanation:

x²+4x-3

x²+4x+4-3-4

(x+2)²-7

=(-2,7)

Answer 2

The turning point of y = x² + 4x - 3 is ( - 2 , - 7 )

Given :

The equation y = x² + 4x - 3

To find :

The turning point of y = x² + 4x - 3 by completing the square

Solution :

Step 1 of 3 :

Write down the given equation

The given equation is

y = x² + 4x - 3

Step 2 of 3 :

Complete the square

$\displaystyle \sf{ y = {x}^{2} + 4x - 3}$

$\displaystyle \sf{ \implies y = {x}^{2} + 4x + 4 - 4- 3}$

$\displaystyle \sf{ \implies y = {x}^{2} + 4x + 4 - 7}$

$\displaystyle \sf{ \implies y = {(x + 2)}^{2} - 7}$

Above is positive quadratic

So minimum value occurs

Step 3 of 3 :

Find turning point

Since ( x + 2)² is non negative

So minimum value of ( x + 2)² is 0 for x = - 2

Consequently for x = - 2 , y = 0 - 7 = - 7

Hence the required turning point = ( - 2 , - 7 )

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