Question

cc.2.2.hs.d.4
find the value of the discriminant. enter only a number.
remember that 0 must be on one side.

y= x² - 12x + 36

Explanation:

Step1: Recall the discriminant formula

For a quadratic equation in the form \(ax^{2}+bx + c = 0\), the discriminant \(D\) is given by \(D=b^{2}-4ac\). First, we need to set the given equation \(y = x^{2}-12x + 36\) to \(0\) (since \(y = 0\) for the quadratic equation to find roots, and discriminant is for quadratic equations in standard form \(ax^{2}+bx + c = 0\)). So we have \(x^{2}-12x + 36=0\). Here, \(a = 1\), \(b=- 12\), and \(c = 36\).

Step2: Substitute values into discriminant formula

Substitute \(a = 1\), \(b=-12\), and \(c = 36\) into the formula \(D=b^{2}-4ac\). So we get \(D=(-12)^{2}-4\times1\times36\).

Step3: Calculate the values

First, calculate \((-12)^{2}=144\) and \(4\times1\times36 = 144\). Then, \(D=144 - 144\).

Step4: Simplify the expression

\(144-144 = 0\).

Answer:

0