The line $y = 4$ intersects the parabola $y = x^2 - 4$ at how many points in the xy-plane?
AZero
BTwo
COne
DInfinitely many
Answer & Solution
Correct answer: B. Two
Set them equal: $4 = x^2 - 4$, so $x^2 = 8$, giving $x = \pm 2\sqrt{2}$. Two real solutions, so the line crosses the parabola at two distinct points.
Related questions
Which expression is equivalent to $3(x + 2) - (x - 4)$?Which expression is equivalent to $\frac{2}{x+1} - \frac{1}{x-2}$?The function $h(x) = a \cdot b^x$ passes through $(0, 12)$ and $(1, 36)$. What is the valuA bacteria culture starts with 80 cells and grows by 25% per hour. Which function models tFor the function $f$, $f(0) = 200$ and $f(x)$ decreases by 50% for each increase of $x$ byIn the xy-plane, the line $y = 5$ intersects the parabola $y = x^2 + bx + 9$ at exactly onHow many distinct real solutions does the equation $(x+2)^2 = -9$ have?What is the minimum value of the function $g(x) = (x-3)^2 + 7$?