How do you identify the important parts of $y = x^{2} - 4 x$ $y= x^2 - 4x$ to graph it?

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How do you identify the important parts of $y = x^{2} - 4 x$ $y= x^2 - 4x$ to graph it?

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Answer 1 · 2015-10-05T00:36:32

Vertex $(2, - 4)$ $(2,-4)$

Axis of symmetry $x = 2$ $x=2$
since the co-efficient of $x^{2}$ $x^2$ is positive, the curve is concave upwards. It has a minimum.

Explanation:

Given -
$y = x^{2} - 4 x$ $y=x^2-4x$
It is a quadratic function of the form $y = x^{2} + b x + c$ $y = x^2+bx+c$
In the given function the constant term is absent.
So we shall have it as '0'.
$y = x^{2} - 4 x + 0$ $y=x^2-4x+0$
The presence or absence of constant term is not going to affect our answer.

Find the vertex
$x = \frac{- b}{2 a} = \frac{- (- 4)}{2 \times 1} = \frac{4}{2} = 2$ $x=(-b)/(2a)=(-(-4))/(2 xx 1)=4/2=2$
$y = 2^{2} - 4 (2) = 4 - 8 = - 4$ $y=2^2-4(2)=4-8=-4$

Vertex $(2, - 4)$ $(2,-4)$

Axis of symmetry $x = 2$ $x=2$
since the co-efficient of $x^{2}$ $x^2$ is positive, the curve is concave upwards. It has a minimum.

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How do you identify the important parts of $y = x^{2} - 4 x$ $y= x^2 - 4x$ to graph it?

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How do you identify the important parts of y=x2−4xy= x^2 - 4x to graph it?

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How do you identify the important parts of $y = x^{2} - 4 x$ $y= x^2 - 4x$ to graph it?