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Anettt [7]
3 years ago
9

- - What is the vertex of the quadratic function f(x) = (x - 6)(x + 2)?

Mathematics
2 answers:
Juliette [100K]3 years ago
6 0

The Standard Form: f(x)=ax^2+bx+c when a, b and c are real numbers and  a must not be 0 (a ≠ 0)

We can convert it in the vertex form which is f(x)=a(x-h)^2+k

f(x)=(x-6)(x+2) Right now, the function takes form of intercepts, we have to convert it to the standard form as we will convert the standard form to vertex.

f(x)=x^2-4x-12 Distributed

f(x)=(x^2-4x)-12\\f(x)=(x^2-4x+4)-12-4

At this part, we can complete the square inside as we'll get (x-h)^2 and k

f(x)=(x-2)^2-16

The vertex is at (2, -16) [The vertex is at (-h, k) so (-(-2), -16) as we get (2, -16)]

kakasveta [241]3 years ago
4 0

Answer:

X=6,x=-2

Step-by-step explanation:

To solve this question we will have to follow the step by step procedure

(x-6)(x+2)

x^2+2x-6x-12

Let's continue

x^2-4x-12

Let's factorise

x^2-6x+2x-12

x(x-6)+2(x-6)

(x-6)(x+2)

so to solve further that is to get the value for x

x-6=0

Add 6 to both sides

x=6

x+2=0

Substrate 2 from both sides

x=-2

Therefore x=6,x=-2

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GuDViN [60]
<h3>Answer:  a = -3 and b = 5</h3>

=================================================

Work Shown:

Multiply top and bottom by \sqrt{2} to rationalize the denominator

\frac{10-\sqrt{18}}{\sqrt{2}}\\\\\frac{\sqrt{2}(10-\sqrt{18})}{\sqrt{2}*\sqrt{2}}\\\\\frac{\sqrt{2}*10-\sqrt{2}*\sqrt{18}}{\sqrt{2*2}}\\\\\frac{\sqrt{2}*10-\sqrt{2*18}}{\sqrt{4}}\\\\\frac{10\sqrt{2}-\sqrt{36}}{2}\\\\\frac{10\sqrt{2}-6}{2}\\\\\frac{-6+10\sqrt{2}}{2}\\\\\frac{2(-3+5\sqrt{2})}{2}\\\\-3+5\sqrt{2}\\\\

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