Write the quadratic equation y= x^2 -6x = 7 in vertex form.
1 answer:
Answer:
(x - 3)² - 16 = 0
Step-by-step explanation:
The equation of a parabola in vertex form is
y = a(x - h)² + k
where (h, k) are the coordinates of the vertex and a is a multiplier
Subtract 7 from both sides
x² - 6x + 7 = 0 ← in standard form
with a = 1, b = - 6
Given a quadratic in standard form then the x- coordinate of the vertex is
= -
= -
= 3
Substitute x = 3 into the equation for y
y = 3² - 6(3) - 7 = 9 - 18 - 7 = - 16 ⇒ (h, k) = (3, - 16)
y = (x - 3)² - 16 = 0
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the point is on the line of direct variation
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-------> substitute ------>
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If a point is on the line of direct variation
then
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<u>case A)</u> point
Substitute the value of x and y in the direct variation equation
-------> is true
therefore
the point is on the line of direct variation
<u>case B)</u> point
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-------> is true
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the point is on the line of direct variation
<u>case C)</u> point
Substitute the value of x and y in the direct variation equation
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therefore
the point is not on the line of direct variation
<u>case D)</u> point
Substitute the value of x and y in the direct variation equation
-------> is true
therefore
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<u>case E)</u> point
Substitute the value of x and y in the direct variation equation
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therefore
the point is not on the line of direct variation
<u>case F)</u> point
Substitute the value of x and y in the direct variation equation
-------> is true
therefore
the point is on the line of direct variation
therefore
<u>the answer is</u>