The parabola has an equation: y=x^2-4x-32.Determine whether the parabola opens up or down; explain your conclusion. Identify the axis of symmetry and the vertex. Identify the minimum. Find the...

The parabola has an equation: y=x^2-4x-32.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.

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justaguide | College Teacher | (Level 2) Distinguished Educator

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The equation of the parabola is y =x^2 - 4x - 32.

To determine the x-intercepts solve x^2 - 4x - 32 = 0

=> x^2 - 8x + 4x - 32 = 0

=> x(x - 8) + 4(x - 8) = 0

=> (x - 8)(x + 4) = 0

=> x = 8 and x = -4

The graph of the parabola is:

It opens upwards.

y = x^2 - 4x - 32

=> y = x^2 - 4x + 4 - 36

=> y = (x - 2)^2 - 36

The axis of symmetry is x = 2

The vertex is (2, -36)

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