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Quadratic equations describe the motion of a baseball after it connects with a bat, and the acceleration of gravity at the Earth's orbit.

# Quadratic Equations Warmup

If $$(x + 4)(3x - 1) = ax^2 + bx + c,$$ what is the value of $$a + b + c?$$

The area of a rectangle can be expressed as $$(2x^2 + 11x - 21).$$ If the width of the rectangle is $$(x + 7),$$ which expression could represent the length?

If $$bx^2 + 32x = 4x(x - a),$$ what is the value of $$ab\, ?$$

The Smith family has $$2,581 \text{ft}^2$$ available in their rectangular backyard to put in a swimming pool. They plan to use the entire space. If the pool will have dimensions of $$20 \text{ft}$$ by $$80 \text{ft}$$, and they want a patio of equal width around the pool, what will be the width of the patio, in feet?

What is the maximum possible area for the rectangle shown?

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