SOLUTION: Find the equation of the parabola when the x intercept is -6, y intercept is 36 and axis of symmetry is x=-6. Can you please help me? Thanks so much in advance

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equation Customizable Word Problems -> SOLUTION: Find the equation of the parabola when the x intercept is -6, y intercept is 36 and axis of symmetry is x=-6. Can you please help me? Thanks so much in advance      Log On


   

Question 703933: Find the equation of the parabola when the x intercept is -6, y intercept is 36 and axis of symmetry is x=-6.
Can you please help me? Thanks so much in advance
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The only way that both the x-intercept and
the axis of symmetry can +-+6+ is if the
parabola just touches the x-axis and thus
only has 1 solution- called a double root.
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If the y intercept is positive, that tells me
the parabola has a minimum and not a maximum.
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If the form is:
+y+=+a%2Ax%5E2+%2B+b%2Ax+%2B+c+
The roots ( x-intercepts ) are given by:
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
When there is a double root,
+b%5E2+=+4%2Aa%2Ac+
+a+=+b%5E2%2F%284c%29+
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The y-intercept occurs at ( 0,36 ), so
+36+=+a%2A0+%2B+b%2A0+%2B+c+
+c+=+36+
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The x-coordinate of the axis of symmetry is at +-b%2F%282a%29+
+-6+=+-b%2F%282a%29+
+b+=+12a+
By substitution:
+b+=+12%2A%28+b%5E2+%2F+%28+4%2A36%29+%29+
+144b+=+12b%5E2+
+b+=+12+
and, since
+b+=+12a+
+a+=+b%2F12+
+a+=+12%2F12+
+a+=+1+
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The equation is
+y+=+x%5E2+%2B+12x+%2B+36+
+y+=+%28+x+%2B+6+%29%5E2+
Here's the plot:
+graph%28+400%2C+400%2C+-14%2C+2%2C+-2%2C+50%2C+%28+x+%2B+6+%29%5E2+%29+