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Rom4ik [11]
2 years ago
8

Express y = -2x² - 4x + 7 in the form of perfect square and find the maximum points.

Mathematics
1 answer:
Marat540 [252]2 years ago
3 0

Answer:

<em>Maximum: (-1,9)</em>

Step-by-step explanation:

<u>Vertex form of the quadratic function</u>

If the graph of the quadratic function has a vertex at the point (h,k), then the function can be written as:

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

Where a is the leading coefficient.

We are given the following function:

y =-2x^2-4x+7

To find the vertex, we need to complete squares. First, factor -2 on the first two terms:

y =-2(x^2+2x)+7

The expression in parentheses must be completed to represent the square of a binomial. Adding 1 and subtracting 1:

y =-2(x^2+2x+1- 1)+7

Taking out the -1:

y =-2(x^2+2x+1)+2+7

Factoring the trinomial and operating:

y =-2(x+1)^2+9

Comparing with the vertex form we have

Vertex (-1,9)

Leading coefficient: -2

Since the leading coefficient is negative, the function has a maximum value at its vertex, i.e.

Maximum: (-1,9)

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2 years ago
The endpoints of RS are R(–5, 12) and S(4, –6). What are the coordinates of point T, which divides RS into a 4:5 ratio?
Ksivusya [100]

Answer:

Option 2 is correct that is (-1,4)

Step-by-step explanation:

We will use the section formula to find the coordinates of T

Formula is (x,y)=\frac{m_1x_2+m_2x_1}{m_1+m_2},\frac{m_1y_2+m_2y_1}{m_1+m_2}

Here, m_1=4,m_2=5,x_1=-5,y_1=12,x_2=4,y_2=-6

On substituting the values in the formula we get

(x,y)=\frac{4\cdot 4+5\cdot -5}{4+5},\frac{4\cdot -6+5\cdot 12}{4+5}

\Rightarrow (x,y)=\frac{4\cdot 4+5\cdot -5}{4+5},\frac{4\cdot -6+5\cdot 12}{4+5}

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\Rightarrow (x,y)=\frac{-9}{9},\frac{36}{9}

\Rightarrow (x,y)=(-1,4)

Therefore, option 2 is correct that is (-1,4)

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