What is the vertex form of #y=7x^2 +3x + 5 #?

Answer 1

#y = 7(x + 3/14)^2 + 917/196#

The vertex form of a quadratic equation #y=ax^2 +bx +c# is #y=a(x+m)^2 +n#, where #m = b/(2a)# and #n = -a(b/(2a))^2 + c# Then the vertex is at the point where the bracketed expression is zero and is therefore #(-m,n)# Therefore #y = 7(x+3/14)^2 -7*9/196 +5# #y = 7(x +3/14)^2 - (63 + 980)/196# #y = 7(x + 3/14)^2 + 917/196#
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Answer 2

The vertex form of the quadratic equation (y = 7x^2 + 3x + 5) is (y = 7(x + \frac{3}{14})^2 + \frac{191}{28}).

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Answer 3

The vertex form of the quadratic function (y = 7x^2 + 3x + 5) is (y = 7(x - h)^2 + k), where ((h, k)) represents the coordinates of the vertex.

To find the vertex form:

  1. Complete the square for the quadratic expression.
  2. Rewrite the expression in the form (y = a(x - h)^2 + k), where (a), (h), and (k) are constants.

Completing the square: [y = 7x^2 + 3x + 5] [y = 7(x^2 + \frac{3}{7}x) + 5]

To complete the square, add and subtract ((\frac{3}{14})^2 = \frac{9}{196}): [y = 7(x^2 + \frac{3}{7}x + \frac{9}{196} - \frac{9}{196}) + 5] [y = 7\left(x + \frac{3}{14}\right)^2 - \frac{9}{28} + 5] [y = 7\left(x + \frac{3}{14}\right)^2 - \frac{9}{28} + \frac{140}{28}] [y = 7\left(x + \frac{3}{14}\right)^2 + \frac{131}{28}]

Therefore, the vertex form of (y = 7x^2 + 3x + 5) is (y = 7\left(x + \frac{3}{14}\right)^2 + \frac{131}{28}).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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