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Klio2033 [76]
4 years ago
8

Write the equation for the quadratic function in standard form

Mathematics
1 answer:
Ede4ka [16]4 years ago
8 0

Answer:

y=x^2+6x+7

Step-by-step explanation:

To write the quadratic in standard form, begin by writing it in vertex form

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

Where (h,k) is the vertex of the parabola.

Here the vertex is (-3,-2). Substitute and write:

y=a(x--3)^2+-2\\y=a(x+3)^2-2

To find a, substitute one point (x,y) from the parabola into the equation and solve for a. Plug in (0,7) a y-intercept of the parabola.

7=a((0)+3)^2-2\\7=a(3)^2-2\\7=9a-2\\9=9a\\1=a

The vertex form of the equation is y=(x+3)^2-2.

To write in standard form, convert vertex form through the distributive property.

y=(x+3)^2-2\\y=(x^2+6x+9)-2\\y=x^2+6x+7

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Step-by-step explanation:

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What is the solution to 3/4b=8
soldier1979 [14.2K]

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b=\frac{32}{3}

Step-by-step explanation:

\frac{3}{4}b=8

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6 0
3 years ago
At the Foremost State Bank the average savings account balance in 2012 was $1900. A random sample of 45 savings account balanes
lakkis [162]

Answer:

The calculated  |t| = |-26.517|=26.517 > 2.326 at 0.01 level of significance

Null hypothesis is rejected at 0.01 level of significance

There is difference between mean savings account balance in 2013 is different from the mean savings account balance in 2012

Step-by-step explanation:

<u><em>Step(i)</em></u>:-

Mean of the Population = 1900

Given random sample size 'n' =  45

Mean of the sample x⁻ = 1000

Standard deviation of the sample = 225

<u><em>Null Hypothesis</em></u>:-

There is no difference between mean savings account balance in 2013 is different from the mean savings account balance in 2012.

<u><em>Alternative Hypothesis</em></u> :-

There is difference between mean savings account balance in 2013 is different from the mean savings account balance in 2012

<u><em>Step(ii</em></u>):-

Test statistic

        t = \frac{x^{-}-mean }{\frac{S.D}{\sqrt{n} } }

        t = \frac{1000-1900 }{\frac{225}{\sqrt{45} } }

       t = -900 /33.54 = -26.517

      |t| = |-26.517|=26.517

Degrees of freedom

                       γ = n-1 = 45-1 =44

t₍₀.₀₁ , ₄₄₎ = 2.326

The calculated  |t| = |-26.517|=26.517 > 2.326 at 0.01 level of significance

Null hypothesis is rejected at 0.01 level of significance

There is difference between mean savings account balance in 2013 is different from the mean savings account balance in 2012

4 0
3 years ago
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