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What is the axis of symmetry and vertex for the graph #y=(2x)^2 - 12x + 17#?

Answer 1

Savannah Anderson

Axis of symmetry#->x= +3/2#

Write as #" "y=4x^2-12x+17#

Now modify it as

#y=4(x^2-12/4x)+17#

Axis of symmetry#->x=(-1/2)xx(-12/4) = +3/2#

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Answer 2

Abigail Allen

To find the axis of symmetry and vertex for the graph of (y = (2x)^2 - 12x + 17):

Axis of symmetry: The axis of symmetry of a quadratic function in the form (y = ax^2 + bx + c) is given by the formula (x = -\frac{b}{2a}). Substitute (a = 2) and (b = -12) into the formula: [x = -\frac{-12}{2(2)} = -\frac{-12}{4} = 3] So, the axis of symmetry is (x = 3).
Vertex: To find the vertex, substitute the value of (x = 3) into the equation (y = (2x)^2 - 12x + 17) to find the corresponding value of (y): [y = (2 \times 3)^2 - 12 \times 3 + 17] [y = (6)^2 - 36 + 17] [y = 36 - 36 + 17] [y = 17] So, the vertex is at the point ((3, 17)).

Therefore, the axis of symmetry is (x = 3) and the vertex is at ((3, 17)).

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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.