The greasiest possible number of intersections for these graphs is 2 if the Mark is solving an equation where one side is a quadratic expression and the other side is a linear expression.
Any equation of the form [tex]\rm ax^2+bx+c=0[/tex] where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic equation.
As we know, the formula for the roots of the quadratic equation is given by:
[tex]\rm x = \dfrac{-b \pm\sqrt{b^2-4ac}}{2a}[/tex]
As we know the standard form of a quadratic equation is:
[tex]\rm Y = \rm ax^2+bx+c[/tex]
And a linear equation can be written as:
y = mx + d
Equating both the expression:
ax² + bx + c = mx + d
ax² + (b-m)x + c - d = 0
The above equation is an also quadratic equation, and we know that the quadratic equation have maximum two roots.
Thus, the greasiest possible number of intersections for these graphs is 2 if the Mark is solving an equation where one side is a quadratic expression and the other side is a linear expression.
Learn more about quadratic equations here:
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