Question

t12 key features of quadratics

1. which graph matches the function ( y = x^2 - 5x + 6 )?

a.
graph a
b.
graph b
c.
graph c
d.
graph d

Explanation:

Step1: Find x-intercepts

Factor the quadratic: \(y = x^2 - 5x + 6=(x - 2)(x - 3)\). Set \(y = 0\), so \(x - 2 = 0\) or \(x - 3 = 0\), giving \(x = 2\) and \(x = 3\). The graph should cross the x - axis at \(x = 2\) and \(x = 3\).

Step2: Find y - intercept

Set \(x = 0\) in \(y=x^2 - 5x + 6\), then \(y=0^2-5\times0 + 6 = 6\). The graph should cross the y - axis at \(y = 6\).

Now, check the options:

• Option A: x - intercepts at \(x = 2\) and \(x = 3\), y - intercept at \(y = 6\).
• Option B: x - intercepts at \(x = 3\) and \(x = 4\) (not 2 and 3), so eliminate.
• Option C: y - intercept at \(y = 3\) (not 6), so eliminate.
• Option D: x - intercepts at \(x = 4\) and \(x = 5\) (not 2 and 3), so eliminate.

Answer:

A. The graph with x - intercepts at \(x = 2\) and \(x = 3\) and y - intercept at \(y = 6\)