y = -1.5; y = x^2 + 8x + a; In the given system of equations, a is a positive constant. The system..

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Bluebook Digital SAT Test 4 Module 2 (Hard) Question 16:

y = -1.5
y = x^2 + 8x + a

In the given system of equations, a is a positive constant. The system has exactly one distinct real solution. What is the value of a?

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Автор

Thank you for the very clear explanations!
A faster way for those scared about the time is to plug it into desmos and find the one point where they touch.

miholovesjdramas
Автор

This problem can be simplified by completing the square.

X^2 + 8x + (a + 1.5) = (x + 4)^2

Equating “c” terms,
a + 1.5 = 16
a = 14.5

If one is interested in the value of x,
x = -4
The value of the vertex.

The completed square is actually in the vertex form with k = 0.

OverclockingCowboy