Megan wants to find the minimum value of the function y = x^2 - 10x + 3. She begins to convert the equation into vertex form by completing the square. Megan stops at the step below.
y = (x + a)^2 + 3 + b
what number should Megan use to replace the a in this equation?
A. 25
B. -10
C. 100
D. -5
well, x^2-10x+25 = (x-5)^2
so I'd pick a = -5
(and b = -25)
So it is -25?
oobleck said -5
the-25 is b
check
y = (x-5)^2 + 3 -25 = x^2 - 10x + 25+ 3 - 25
= x^2 - 10 x +3
To convert the equation y = x^2 - 10x + 3 into vertex form by completing the square, we need to rewrite it as y = (x + a)^2 + 3 + b, where a and b are constants to be determined.
To find the value of a, note that the vertex form of a quadratic function is given by y = (x - h)^2 + k, where (h, k) represents the coordinates of the vertex.
To find the value of a, we need to determine the value of h in the vertex form. In the given equation, we have x^2 - 10x + 3. To complete the square, we need to take half of the coefficient of x (which is -10) and square that value.
The value of a can be determined by taking half of -10, which is -5, and replacing it with the x term in the equation. Therefore, Megan should use -5 to replace a in the equation.
So, the correct answer is D. -5.