Pretty much we've been given four equations.
1. y= 2x^2 -7x - 3
2. y= -3x^2+6x-1
3. y= x^2+x+4
4. y= 4x^2 -12x + 9
We've also been given four graphs and told to match them. Looking at the equations and the graphs it is easy to see which ones relate however we have to use the quadratic equation to prove it, I guess. Everytime I do it, I figure out 1. but then 2. doesn't work. I get the x-intercepts as -1.32 and 0.32 but none of the graphs match with it. I don't know what i'm doing wrong.
The formula is -b+ or - sqroot of b^2-4ac / 2a
Help explain where I'm going wrong because I also used Graphmatica and it shows the correct answers. :l
1. y= 2x^2 -7x - 3
2. y= -3x^2+6x-1
3. y= x^2+x+4
4. y= 4x^2 -12x + 9
We've also been given four graphs and told to match them. Looking at the equations and the graphs it is easy to see which ones relate however we have to use the quadratic equation to prove it, I guess. Everytime I do it, I figure out 1. but then 2. doesn't work. I get the x-intercepts as -1.32 and 0.32 but none of the graphs match with it. I don't know what i'm doing wrong.
The formula is -b+ or - sqroot of b^2-4ac / 2a
Help explain where I'm going wrong because I also used Graphmatica and it shows the correct answers. :l
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I will give one example and you need to do the rest!
1. y= 2x^2 -7x - 3
x = [ - b ± √ ( b ² - 4 a c ) ] / 2 a
x = [ - (-7) ± √ ( (-7) ² - 4 * 2 * (-3) ) ] / (2 * 2)
x = [ 7 ± √ ( 49 + 4 * 2 * 3 ) ] / 4
x = [ 7 ± √ ( 49 + 24 ) ] / 4
x = [ 7 ± √73 ] / 4
x = 3.886 or -0.386
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2. y= -3x^2+6x-1
x = [ - b ± √ ( b ² - 4 a c ) ] / 2 a
x = [ -6 ± √ ( 6 ² - 4 * (-3) * (-1) ) ] / [2 * (-3)]
x = [ -6 ± √ ( 36 - 12) ] / (-6)
x = [ -6 ± √24 ] / (-6)
x = [ -6 ± 2√6 ] / (-6)
x = [ -3 ± √6 ] / (-3)
x= 1.8165 or 0.1835
1. y= 2x^2 -7x - 3
x = [ - b ± √ ( b ² - 4 a c ) ] / 2 a
x = [ - (-7) ± √ ( (-7) ² - 4 * 2 * (-3) ) ] / (2 * 2)
x = [ 7 ± √ ( 49 + 4 * 2 * 3 ) ] / 4
x = [ 7 ± √ ( 49 + 24 ) ] / 4
x = [ 7 ± √73 ] / 4
x = 3.886 or -0.386
=============================
2. y= -3x^2+6x-1
x = [ - b ± √ ( b ² - 4 a c ) ] / 2 a
x = [ -6 ± √ ( 6 ² - 4 * (-3) * (-1) ) ] / [2 * (-3)]
x = [ -6 ± √ ( 36 - 12) ] / (-6)
x = [ -6 ± √24 ] / (-6)
x = [ -6 ± 2√6 ] / (-6)
x = [ -3 ± √6 ] / (-3)
x= 1.8165 or 0.1835
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the answer for 2 is
x=[-6±√(36-12)]/-6
x=0.1835
x=1.8165
3. y= x^2+x+4
x=[-2±√(1-16)]/2 no real solution
x=-0.5+1.9365i
x=-0.5-1.9365i
4. y= 4x^2 -12x + 9
x=[12±√(144- 144)]/8
x=1.5
x=[-6±√(36-12)]/-6
x=0.1835
x=1.8165
3. y= x^2+x+4
x=[-2±√(1-16)]/2 no real solution
x=-0.5+1.9365i
x=-0.5-1.9365i
4. y= 4x^2 -12x + 9
x=[12±√(144- 144)]/8
x=1.5
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y = (- b +- sqrt(b^2 - 4ac)))/2a
y = (- 6 +- sqrt(36 - 4(- 1)(6))/(- 6)
y = (- 6 +- sqrt(36 + 24))(- 6)
y = (- 6 +- sqrt(60))/(- 6)
y = (- 6 +- sqrt(4)sqrt(15))/(- 6)
y = 1 +- 1/3sqrt(15)
y = 1 +- 3.87/3
y = 1 + 1.29 or 1 - 2.29
y = 2.29 or - 1.29
y = (- 6 +- sqrt(36 - 4(- 1)(6))/(- 6)
y = (- 6 +- sqrt(36 + 24))(- 6)
y = (- 6 +- sqrt(60))/(- 6)
y = (- 6 +- sqrt(4)sqrt(15))/(- 6)
y = 1 +- 1/3sqrt(15)
y = 1 +- 3.87/3
y = 1 + 1.29 or 1 - 2.29
y = 2.29 or - 1.29
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for #2,
-b+ or - sqroot of b^2-4ac / 2a
= (-6+or- sqrt of (6^2-4*3))/(2*-3)
= (-6+ or - 2*sq rt of 6)/-6
= (3 + or - sqrt of 6)/3
= 1.817 or 0.184
-b+ or - sqroot of b^2-4ac / 2a
= (-6+or- sqrt of (6^2-4*3))/(2*-3)
= (-6+ or - 2*sq rt of 6)/-6
= (3 + or - sqrt of 6)/3
= 1.817 or 0.184
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2. x = [-6±√(36-12)]/(-6) = (6±2√6)/6 ≈ 1.816, 0.184