How do you find the important points to graph $f (x) = 2 x^{2}$ $f(x)=2x^2$ ?

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How do you find the important points to graph $f (x) = 2 x^{2}$ $f(x)=2x^2$ ?

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Answer 1 · 2018-07-10T15:38:49

See explanation

Explanation:

Set $y = f (x) = 2 x^{2}$ $y=f(x)=2x^2$

Compare to the standardised form: $y = a x^{2} + b x + c$ $y=ax^2+bx+c$
This equation $dddddfdd \to ddddd y = 2 x^{2} + 0 x + 0$ $color(white)("dddddfdd") ->color(white)("ddddd")y=2x^2+0x+0$

Key points:

$a > 0 \to (positive)$ $a>0 -> ("positive")$ so the graph is of form $\cup$ $uu$

$c \to$ $c->$ y-intercept $= 0$ $=0$

$x_{vertex} \to (- \frac{1}{2}) \times \frac{b}{a} ddd = ddd (- \frac{1}{2}) \times \frac{0}{2} d = d 0$ $x_("vertex") -> (-1/2)xx b/acolor(white)("ddd") =color(white)("ddd") (-1/2)xx0/2color(white)("d")=color(white)("d")0$
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As $x_{vertex} = 0$ $x_("vertex")=0$ the axis of symmetry is the y-axis

As $a > 0$ $a>0$ then the general shape is $\cup$ $uu$ with the y-axis in the middle.

Couple this with $c = 0$ $c=0$ and it means that the vertex is at $(x, y) = (0.0)$ $(x,y)=(0.0)$

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How do you find the important points to graph $f (x) = 2 x^{2}$ $f(x)=2x^2$ ?

1 Answer

Explanation:

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How do you find the important points to graph $f (x) = 2 x^{2}$ $f(x)=2x^2$ ?