QQuestionMathematics
QuestionMathematics
"Convert the quadratic equation from standard form to vertex form
y=-x^2 - 14x- 59"
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Answer
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Step 1:: Identify the coefficients a, b, and c from the given quadratic equation in standard form.
The quadratic equation is given as y = -x^2 - 14x - 59. Here, the coefficient a is - 1, the coefficient b is - 14, and the constant term c is - 59.
Step 2:: Calculate the vertex of the parabola using the formula for the x-coordinate of the vertex, h = -b/(2a).
h = -(- 14)/(2 *- 1) h = 14 / 2 h = 7
Step 3:: Find the y-coordinate of the vertex using the value of h and the given quadratic equation.
Substitute x = 7 into the given quadratic equation: y = -(7)^2 - 14 *(7) - 59 y = - 49 - 98 - 59 y = - 206 So, the vertex of the parabola is at (7, - 206).
Step 4:: Rewrite the quadratic equation in vertex form, y = a*(x-h)^2 + k, where h is the x-coordinate of the vertex and k is the y-coordinate of the vertex.
y = - 1 *(x- 7)^2 - 206
Final Answer
The quadratic equation in vertex form is y = - 1 *(x- 7)^2 - 206.
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