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3 years ago

What is the minimum point of the equation x^2+19=9x

Mathematics

1 answer:

azamat3 years ago

3 0

Answer:

The minimum point is (4.5, -1.25).

Step-by-step explanation:

x^2+19=9x

= x^2 - 9x + 19 = 0

Convert to Vertex form:

(x - 4.5)^2 - 4.5^2 + 19 = 0

= (x - 4.5)^2 - 1.25.

The minimum point is (4.5, -1.25).

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<h2>Perfect Squares</h2>

Perfect square formula/rules:

$a^2+2ab+b^2=(a+b)^2$
$a^2-2ab+b^2=(a-b)^2$

Trinomials are often organized like $ax^2+bx+c$ .

The <em>b</em> value in this case is <em>c</em>, and it will always equal the square of half of the <em>b</em> value.

Perfect square trinomial: $ax^2+bx+(\dfrac{b}{2})^2$
or $ax^2-bx+(\dfrac{b}{2})^2$

<h2>Solving the Question</h2>

We're given:

$c^2-4c$

In a trinomial, we're given the $ax^2$ and $bx$ values. <em>a</em> in this case is 1 and <em>b</em> in this case is 4. To find the third value by dividing 4 by 2 and squaring the quotient:

4 ÷ 2 = 2
2² = 4

Therefore, the term that we can add is + 4.

$c^2-4c+4$

To write this as the square of a bracketed expression, we can follow the rule $a^2-2ab+b^2=(a-b)^2$ :

$(c-2)^2$

<h2>Answer</h2>

$c^2-4c+4$

$(c-2)^2$

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1 year ago