Question

solve graphically Y=x^2-4x+5​

Answer 1

Answer:

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Step-by-step explanation:

This is a quadratic function of form  

y

=

a

x

2

+

b

x

+

c

, with a=1, b=-4 and c=-5.

The graph will be a parabola.

Since a is positive, the arms go up.

To find the y-intercept, let x = 0 and find y = c = -5.

To find the x-intercepts, let y = 0 and use either factorizing or the quadratic formula to find the roots x = 5 or x = -1.

To find the turning point, set the derivative to zero.

∴

2

x

−

4

=

0

⇒

x

=

2

>

Then find y(2) = -9.

Then put all of this together to draw the graph as shown below :

graph{x^2-4x-5 [-22.49, 22.5, -11.24, 11.26]}