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adelina 88 [10]

3 years ago

11

Determine whether the ordered pair is a solution of the linear equation. thanks in advance!!

1 answer:

eduard3 years ago

4 0

Answer:

no

Step-by-step explanation:

because it is nor a solution

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HURRYYYYYYYYY!! What is the equation of the quadratic function with a vertex at (2, 25) and an x-intercept at (7,0)?

tangare [24]

Answer:

$y=-(x-7)(x+3)$

which is none of the choices provided.

Are you sure the question is right or even the choices?

You can even write it as:

$y=-(x+3)(x-7)$ but this is still not a choice.

Step-by-step explanation:

The vertex form of a quadratic is $y=a(x-h)^2+k$ .

This is called vertex form because it gives you the vertex is $(h,k)$ .

We are given that $(h,k)=(2,25)$ which makes our equation:

$y=a(x-2)^2+25$ .

We can find the value of $a$ by plugging in the x-intercept (7,0) for $(x,y)$ into:

$y=a(x-2)^2+25$

$0=a(7-2)^2+25$

$0=a(5)^2+25$

Subtract 25 on both sides:

$-25=a(5)^2$

$-25=a(25)$

Divide both sides by 25:

$\frac{-25}{25}=a$

$-1=a$ .

So the equation for the quadratic is:

$y=-1(x-2)^2+25$

Let's put this into factored form since all the choices are in factored form.

This will require us to multiply the (x-2)(x-2) out:

$y=-1(x-2)(x-2)+25$

$y=-1(x^2-2x-2x+4)+25$

$y=-1(x^2-4x+4)+25$

$y=-x^2+4x-4+25$

$y=-x^2+4x+21$

Factor out -1:

$y=-(x^2-4x-21)$

WE need to find two numbers that multiply to be -21 and add to be -4:

$y=-(x-7)(x+3)$

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