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`y=x^2-4x-32`       (a) Determine whether the parabola opens up or down. (b) Identify the axis of symmetry. (c) Identify the minimum point. (d) Find the x-intercepts.     determine whether the parabola opens up or down; explain your conclusion. identify the axis of symmetry and the vertex. identify the minimum. find the x-intercepts by factoring. show how the value of the discriminant supports your conclusions of the x-intercepts by factoring.

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(a) The sign of  a (coefficient of x^2) determines direction of the parabola. If a is positive. the parabola opens. And if negative, it opens down.

Since a=+1, hence the paranbola opens up.

(b) When the parabola  is either upward or downward, its axis of symmetry is the x-coordinate of the vertex(h,k), where `h=-b/(2a)` . So,

`h=-b/(2a)= -(-4)/(2*1)=2`

Thus, the axis of symmetry is `x=2` .

(c) The minimum point of the parabola is the vertex (h,k). To solve for k, substitute...

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