Iwould appreciate the the graph of y = x2 –7x +12 is a parabola with x-intercepts at: {-3 and -4, or 3 and 4} and a vertex that is the: {lowest or highest} point on the curve. in advance!

the x-intercepts are

The vertex is the lowest point on the curve

Step-by-step explanation:

we know that

The equation of a vertical parabola in vertex form is equal to

where

(h,k) is the vertex of the parabola

if -----> then the parabola open upward (vertex is a minimum)

if -----> then the parabola open downward (vertex is a maximum)

In this problem we have

so

the parabola open upward (vertex is a minimum)

Find the x-intercepts of the quadratic equation

Equate the equation to zero

Group terms that contain the same variable, and move the constant to the opposite side of the equation

Complete the square. Remember to balance the equation by adding the same constants to each side

Rewrite as perfect squares

square root both sides

therefore

the x-intercepts are

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