Use the Completing the Square method to find the vertex form of the quadratic function y = x^2 + 7x + 12?
回答 (10)
2008-12-24 4:08 pm
✔ 最佳答案
Equation: x^2+7x+12(x^2+7 x)+12
(x^2+7 x+(7/2)^2)+12-1(7/2)^2
(x+7/2)^2+12-49/4
(x+7/2)^2-1/4
y=(x+7/2)^2-1/4
vertex is (-7/2, -1/4)
2016-10-18 6:13 pm
y = x² + 5x + 12 y - 12 = x² + 5x The coefficient of the x term is 5. comprehensive the sq. employing (5/2)² y - 12 + (5/2)² = x² + 5x + (5/2)² y - 12 + (25/4) = (x+5/2)² y + 13/4 = (x+5/2)² that's the equation of an up-beginning off parabola with vertex at (-5/2,-13/4)
2008-12-24 8:49 pm
a=1 b=7 c=12
1st, find the axis of symmetry (aos)
x=-b/2a
x= -(7)/2(1)
x=-7/2
aos= -7/2
Plug in x in the quadratic equation
(-7/2)^2+7(-7/2)+12= -1/4
Vertex= (-7/2, -1/4)
1st, find the axis of symmetry (aos)
x=-b/2a
x= -(7)/2(1)
x=-7/2
aos= -7/2
Plug in x in the quadratic equation
(-7/2)^2+7(-7/2)+12= -1/4
Vertex= (-7/2, -1/4)
2008-12-24 4:39 pm
y = (x = (7 / 2))^2 + 12 - (49 / 4)
y = (x + (7 / 2)^2 - (1 / 4)
y = (x + (7 / 2)^2 - (1 / 4)
2008-12-24 4:24 pm
y = ( x² + 7x + 49/4) + 12 - 49/4
y = (x + 7/2)² - 1/4
Vertex V (- 7/2 , -1/4)
y = (x + 7/2)² - 1/4
Vertex V (- 7/2 , -1/4)
2008-12-24 4:13 pm
x^2 + 7x + 12 = y
x^2 + 7x = y - 12
x^2 + 7x/2 + 7x/2 = y - 12
x^2 + 7x/2 + 7x/2 + 49/4 = y - 12 + 49/4
(x^2 + 7x/2) + (7x/2 + 49/4) = (4y - 48)/4 + 49/4
x(x + 7/2) + 7/2(x + 7/2) = (4y - 48 + 49)/4
(x + 7/2)(x + 7/2) = (4y + 1)/4
(x + 7/2)^2 = 4y/4 + 1/4
(x + 7/2)^2 = y + 1/4
∴ the vertex is (-7/2 , -1/4)
x^2 + 7x = y - 12
x^2 + 7x/2 + 7x/2 = y - 12
x^2 + 7x/2 + 7x/2 + 49/4 = y - 12 + 49/4
(x^2 + 7x/2) + (7x/2 + 49/4) = (4y - 48)/4 + 49/4
x(x + 7/2) + 7/2(x + 7/2) = (4y - 48 + 49)/4
(x + 7/2)(x + 7/2) = (4y + 1)/4
(x + 7/2)^2 = 4y/4 + 1/4
(x + 7/2)^2 = y + 1/4
∴ the vertex is (-7/2 , -1/4)
2008-12-24 4:11 pm
Hi,
y = x² + 7x + 12
y = x² + 7x + __ + 12
½(7) = 3.5 and 3.5² = 12.25
y = (x² + 7x + 12.25) + 12 - 12.25
y = (x + 3.5)² - .25 <==ANSWER
I hope that helps!! :-)
Merry Christmas!!
y = x² + 7x + 12
y = x² + 7x + __ + 12
½(7) = 3.5 and 3.5² = 12.25
y = (x² + 7x + 12.25) + 12 - 12.25
y = (x + 3.5)² - .25 <==ANSWER
I hope that helps!! :-)
Merry Christmas!!
2008-12-24 4:10 pm
y = x^2 + 7x + 12
y - 12 = x^2 +7x
y -12 + 49/4 = x^2 + 7x + 49/4
y +1/4 = (x+7/2)^2
so vertex V is at (-7/2, -1/4) (answer)
y - 12 = x^2 +7x
y -12 + 49/4 = x^2 + 7x + 49/4
y +1/4 = (x+7/2)^2
so vertex V is at (-7/2, -1/4) (answer)
2008-12-24 4:05 pm
y = (x+3.5)^2-2.5
2008-12-24 4:08 pm
(x+4)(x+3)
收錄日期: 2021-05-01 11:39:55
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