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11111nata11111 [884]
2 years ago
13

Sketch f(x) = 5x2 - 20 labelling any intercepts.​

Computers and Technology
1 answer:
Norma-Jean [14]2 years ago
8 0

Answer:

  • The graph of the function is attached below.
  • The x-intercepts will be: (2, 0), (-2, 0)
  • The y-intercept will be: (-20, 0)

Explanation:

Given the function

f\left(x\right)\:=\:5x^2-\:20

As we know that the x-intercept(s) can be obtained by setting the value y=0

so

y=\:5x^2-\:20

switching sides

5x^2-20=0

Add 20 to both sides

5x^2-20+20=0+20

5x^2=20

Dividing both sides by 5

\frac{5x^2}{5}=\frac{20}{5}

x^2=4

\mathrm{For\:}x^2=f\left(a\right)\mathrm{\:the\:solutions\:are\:}x=\sqrt{f\left(a\right)},\:\:-\sqrt{f\left(a\right)}

x=\sqrt{4},\:x=-\sqrt{4}

x=2,\:x=-2

so the x-intercepts will be: (2, 0), (-2, 0)

we also know that the y-intercept(s) can obtained by setting the value x=0

so

y=\:5(0)^2-\:20

y=0-20

y=-20

so the y-intercept will be: (-20, 0)

From the attached figure, all the intercepts are labeled.

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