Select all of the quadratic expressions in vertex form.

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Final answer:

The quadratic expressions in vertex form are (a) (x-1)²+10 and (c) (x-5)². These expressions follow the form a*(x-h)² + k, which is the standard form for a quadratic equation in vertex form.

Explanation:

The question asks to select all the quadratic expressions in vertex form. The vertex form of a quadratic equation is given by a*(x-h)² + k. Here, (h, k) is the vertex of the parabola. Let's examine the given options:

• (a) (x-1)²+10: The expression can be rewritten as 1*(x-1)² + 10, which is in vertex form.
• (b) (x-5)(x-4): This is not in vertex form, it is a factored form of quadratic equation.
• (c) (x-5)²: This is in vertex form with a = 1, h = 5 and k = 0.
• (d) x²-4x+4: This is standard form, not vertex form.
• (e) x(x-4): This is not in vertex form, it is a factored form of quadratic equation.

So, the quadratic expressions in vertex form are options (a) (x-1)²+10 and (c) (x-5)².

Learn more about Vertex Form here:

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Complete question:

Select all of the quadratic expressions in vertex form

a) (x-1)²+10

b) (x-5)(x-4)

c) (x-5)²

d) x²-4x+4

e) x(x-4)

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Final answer:

The quadratic expressions in vertex form in the given options are (x-1)^2+10 and (x-5)^2. The vertex form of a quadratic expression is a*(x-h)^2 + k, where a, h, and k are constants.

Explanation:

The quadratic expressions in vertex form among the given options are a) (x-1)^2+10 and c) (x-5)^2. In general, a quadratic expression is in vertex form if it is written as a*(x-h)^2 + k, where a, h, and k are constants, and h and k represent the vertex of the parabola.

In other words, the vertex form provides an efficient way to identify the vertex of a parabola, as represented by a quadratic equation, and provides the easiest way to graph such an equation. The other expressions b) (x-5)(x-4), d) x^2-4x+4, and e) x(x-4) are not in vertex form.

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