Write the quadratic function in the form f (x) = a (x - h)2 + k. Then, give the vertex of its graph.
f (x) = – 2x² + 16x – 30

Writing in the form specified: f(x)=???

Vertex: (?,?)

The vertex form is:

Where the vertex of the function is (4, 2).

Step-by-step explanation:

We want to find the vertex and the vertex form of the quadratic function:

We have two methods of converting from standard form to vertex form: (1) by using the vertex formulas or (2) by completing the square.

Method 1) Using Formulas:

First, note that the leading coefficient of our function is -2.

The vertex of a quadratic equation is given by the formulas:

In this case, a = -2, b = 16, and c = -30. Find the x-coordinate of the vertex:

In order to find the y-coordinate of the vertex, we substitute this value back in. Hence:

Therefore, our vertex is (4, 2).

Vertex form is:

Where a is the leading coefficient and (h, k) is the vertex.

Substitute. Our leading coefficient is -2 and our vertex is (4, 2). Therefore:

Method 2) Completing the Square:

To complete the square, we first factor out the leading coefficient from the first two terms:

Then, we divide the coefficient of the b term by half and square it. This yields:

We will add this value inside of the parentheses. Since we added 16 inside the parentheses, we will subtract 16 outside of the parenthese to remain the equality of the function. However, since the parentheses is multiplied by -2, we technically added -2(16) = -32 inside. So, we will subtract -32 outside. Thus:

Simplify:

Factor using the perfect square trinomial:

We acquire the same result.

answer: median

step-by-step explanation:

the median is the middle value when a data set is ordered from least to greatest

d) by the cross product property, ab^2 = bc multiplied by ad

step-by-step explanation:

we are given

in the given triangle abc

angle a is 90° and segment ad is perpendicular to segment bc

we can see that

triangle(abc) and triangle(abd) are similar because they have common side and same angle (90 degree)

so, triangles(abc) and abd are similar

since, they are similar

so, the ratio of their sides must be equal

we get

now, we can cross multiply

and we get

so, this could be step to prove it