EM-2033

Solving equations graphically

E Math · Secondary 4 · Hard · Solving equations graphically

Consider the equation

-0.25x^2 + x + 2 = k

, where

k

is a constant. Which statement about the graph of

y = -0.25x^2 + x + 2

and the horizontal line

y = k

is correct?

The number of real solutions equals the number of intersection points of the curve and the line $y = k$
There are always exactly two real solutions for any value of $k$
There is at most one real solution for any value of $k$
The equation has no real solutions for any value of $k$

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