Question

section 3: functions and statistics
29.
which equation could represent a graph with x-intercepts of (4,0) and (-7, 0)?
a ( y = x^2 + 3x - 28 )
b ( y = x^2 - 3x - 28 )
c ( y = x^2 + 3x + 28 )
d ( y = x^2 - 3x + 28 )

Explanation:

Step1: Recall factored form of quadratic

If a quadratic has x - intercepts at \(x = a\) and \(x = b\), its factored form is \(y=(x - a)(x - b)\). Here, \(a = 4\) and \(b=-7\), so \(y=(x - 4)(x+7)\).

Step2: Expand the factored form

Expand \((x - 4)(x + 7)\):
\(x(x + 7)-4(x + 7)=x^{2}+7x-4x-28=x^{2}+3x - 28\).

Answer:

A. \(y = x^{2}+3x - 28\)