Quadratic equation in vertex form?

May 2021 3 67 Report

Quadratic equation in vertex form?

I need to convert this equation into a vertex form, I do not really understand the method that you must use to do this, if you could describe it and tell me what it is called and give step by step on how to do this problem, that would be great.

y=-3x^2+12x-15

Science & Mathematics / Mathematics

Lucy

Verified answer

y = -3x² + 12x - 15

Group.

y = (-3x² + 12x) - 15

Factor

y = -3(x² - 4x) - 15

Add placeholders.

y = -3(x² - 4x + ___) - 15 + 3(___)

Notice that the second blank is multiplied by 3 to account for what you had to factor out.

Take the coefficient of the x term: -4

Divide it by 2: -4 / 2 = -2

Square it: (-2)² = 4

Add 4 to both blanks.

y = -3(x² - 4x + 4) - 15 + 3(4)

x² - 4x + 4 is the expanded form of a perfect square binomial.

Remember that (a - b)² = a² - 2ab + b². Apply this to what you have.

y = -3(x² - 4x + 4) - 15 + 3(4)

y = -3(x - 2)² - 15 + 3(4)

Simplify the rest.

y = -3(x - 2)² - 15 + 12

y = -3(x - 2)² - 3

ANSWER: y = -3(x - 2)² - 3 is the vertex form.

BONUS: This means that the vertex is at (2, -3).

HINT: Remember that the vertex form is: y = a(x - h)² + k

CHECK:

y = -3(x - 2)² - 3

y = -3[(x)² + 2(x)(-2) + (-2)²] - 3

y = -3(x² - 4x + 4) - 3

y = -3(x²) - 3(-4x) - 3(4) - 3

y = -3x² + 12x - 12 - 3

y = -3x² + 12x - 15

TRUE

y= -x^2-10x-9 y= (-x^2-10x)-9 y= -(x^2+10x)-9 y= -(x^2+10x+25)-9+25 considering you subtract 25 interior, upload it back exterior. y = -(x+5)^2 + sixteen Downward commencing up parabola with vertex at (-5, sixteen) Neither of your published solutions is sweet, observe the damaging exterior the factored trinomial.