Digital SAT Math Test 2 Question 11

In the

x y

-plane, a line with equation

y = 3 a

, for some constant

a

, intersects a parabola at exactly one point. If the parabola has equation

y = x^{2} - 4 x - 5

, what is the value of

a

Answer:

Answer:

-3

Explanation

The correct answer is $- 3$ .

Substitute $y$ from the first equation into the second equation and then find $a$ for which there is exactly one solution for the equation.

A quadratic equation has no real root if the discriminant, $D = b^{2} - 4 a c$ , is less than zero.

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