Write in the form p(x +q)² + r... 5x² + 9x +4

Question

asked Sep 12, 2023 170k views

2 Answers

Tajihiro · Answer 1 · 2023-09-18T04:02:06+0000

Answer:

$5\left(x+(9)/(10)\right)^2-(1)/(20)$

Explanation:

Given:

5x^2+9x+4

Factor out the coefficient of the leading term from the first two terms:

$\implies 5\left(x^2+(9)/(5)x\right)+4$

Add the square of half the coefficient of the x term inside the parentheses and subtract its distributed value from the expression:

$\implies 5\left(x^2+(9)/(5)x+\left(\frac{(9)/(5)}2\right)^2\right)+4-5\left(\frac{(9)/(5)}2\right)^2$

Simplify:

$\implies 5\left(x^2+(9)/(5)x+\left((9)/(10)\right)^2\right)+4-5\left((9)/(10)\right)^2$

$\implies 5\left(x^2+(9)/(5)x+(81)/(100)\right)+4-5\left((81)/(100)\right)$

$\implies 5\left(x^2+(9)/(5)x+(81)/(100)\right)+4-(405)/(100)$

$\implies 5\left(x^2+(9)/(5)x+(81)/(100)\right)-(1)/(20)$

Factor the perfect trinomial contained within the parentheses:

$\implies 5\left(x+(9)/(10)\right)^2-(1)/(20)$

Therefore, the given expression written in vertex form is:

$5\left(x+(9)/(10)\right)^2-(1)/(20)$