Question

A quadratic inequality contains the values greater than or equal to the quadratic function that has a vertex of -3,12 and contains the point -2,15 on the boundary. A student uses the vertex formto write the equation in standard form. her work is shown

y = 3(x+3)² + 12 y = 3(x²+9) + 12 y = 3x² + 39

which statment is true about the student
a. the student should subtract 3 from x, instead of adding 3. .

Answer 1

The student made an error while expanding the binomial during the conversion from vertex form to standard form of a quadratic equation. The correct expansion of (x + 3)^2 is x^2 + 6x + 9, leading to the standard form y = 3x^2 + 18x + 39.

Step-by-step explanation:

The student is converting a quadratic equation from vertex form to standard form. In this process, they should expand and simplify correctly to obtain the standard form of the quadratic equation. However, the student has made an error in the expansion part of the process. Specifically, when they squared the binomial (x + 3), they should have applied the formula (a + b)^2 = a^2 + 2ab + b^2 but incorrectly used (x^2 + 9) instead of (x^2 + 6x + 9).

Therefore, the correct expansion would be:

• y = 3(x + 3)^2 + 12
• y = 3(x^2 + 6x + 9) + 12
• y = 3x^2 + 18x + 27 + 12
• y = 3x^2 + 18x + 39

This quadratic inequality is now accurately represented in standard form, which is generally written as ax^2 + bx + c, where a, b, and c are constants.