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stich3 [128]
3 years ago
5

the vertex of a quadratic function is (6, 2), and the y-intercept of the function is (0, −70). the equation of the function in v

ertex form, f(x) = a(x - h)2 k, is shown. –70 = a(0 – 6)2 2 what is the value of a?
Mathematics
2 answers:
Kamila [148]3 years ago
6 0

<u>Answer-</u>

<em>The value of a is </em><em>-2</em>

<u>Solution-</u>

The vertex form of parabola-

y=a(x-h)^2+k

Where, vertex is at (h, k)

Given that the vertex is at (6, 2), so equation would be

y=a(x-6)^2+2

As the y intercept is the point which lies on the parabola, so it must satisfy the parabola equation.

\Rightarrow -70=a(0-6)^2+2

\Rightarrow -70-2=a(-6)^2

\Rightarrow a(6)^2=-72

\Rightarrow 36a=-72

\Rightarrow a=-2

My name is Ann [436]3 years ago
5 0
Hello,
++++++++++++++++
f(x)=a(x-6)²+2
f(0)=-70==>a(-6)²+2=-70===>36a=-72==>a=-2
++++++++++++++++++++

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Step-by-step explanation:

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Help even tho it’s multiple choice make sure you are correct... I beg you lol
kondaur [170]

Answer:

The equation of the line is:

y=(-\frac{1}{2})x+1

Therefore, option a is the correct answer.

Step-by-step explanation:

Given the points

  • (-2, 2)
  • (4, -1)

Finding the slope

\mathrm{Slope\:between\:two\:points}:\quad \mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}

\left(x_1,\:y_1\right)=\left(-2,\:2\right),\:\left(x_2,\:y_2\right)=\left(4,\:-1\right)

m=\frac{-1-2}{4-\left(-2\right)}

m=-\frac{1}{2}

As the point-slope form of the equation of the line is

y-y_1=m\left(x-x_1\right)

where m is the slope

substituting the values m=-\frac{1}{2} and the point (-2, 2)

y-y_1=m\left(x-x_1\right)

y-2=\frac{-1}{2}\left(x-\left(-2\right)\right)

y-2=\frac{-1}{2}\left(x+2\right)

y-2=-\frac{1}{2}\left(x+2\right)       ∵\mathrm{Apply\:the\:fraction\:rule}:\quad \frac{-a}{b}=-\frac{a}{b}

Add 2 to both sides

y-2+2=-\frac{1}{2}\left(x+2\right)+2

y=(-\frac{1}{2})x+1

Hence, the equation of the line is:

y=(-\frac{1}{2})x+1

Therefore, option a is the correct answer.

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Step-by-step explanation:

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