Question

Convert x-intercept form to standard form.

a) y = a(x - p)(x - q)
b) y = a(x + p)(x - q)
c) y = a(x - p)(x + q)
d) y = a(x + p)(x + q)

Answer 1

Convert x-intercept form to standard form by multiplying the factors and combining like terms to obtain a polynomial in the form y = ax^2 + bx + c.

Step-by-step explanation:

The student is asking to convert the x-intercept form of a quadratic equation to standard form. The four given equations are different variations of a quadratic equation, which typically represents a parabola on a graph. We know that the standard form of a quadratic equation is y = ax^2 + bx + c, where a, b, and c are constants, and x and y are variables.

• For equation (a) y = a(x - p)(x - q), we multiply the factors to get the standard form: y = ax^2 - a(p + q)x + apq.
• For equation (b) y = a(x + p)(x - q), we similarly multiply the factors: y = ax^2 + a(q - p)x - apq.
• For equation (c) y = a(x - p)(x + q), again multiplying the factors gives us: y = ax^2 + a(p - q)x - apq.
• For equation (d) y = a(x + p)(x + q), multiplying the factors yields: y = ax^2 + a(p + q)x + apq.

It is important to multiply out the factors carefully and combine like terms to arrive at the correct standard form for each equation.