Question

What is the standard form of the equation of a parabola is y = 5x^2 + 20x + 14. What is the vertex form of the equation

Answer 1

vertex form is $y=a(x-h)^2+k$

comlpete the square

$y=5x^2+20x+14$

group x terms

$y=(5x^2+20x)+14$

factor quadratic coefient

$y=5(x^2+4x)+14$

take 1/2 of linear coefient and square it

4/2=2, 2^2=4

add positive and negative of it inside the parentheasees

$y=5(x^2+4x+4-4)+14$

factor perfect squarer trinomial

$y=5((x+2)^2-4)+14$

expand

$y=5(x+2)^2-20+14$

$y=5(x+2)^2-6$ is vertex form