Question

match the following
$y = -2 (x + 4) (x - 7)$ $y = 2x^2 - 3x + 5$
standard form vertex form intercept (factored) form
$y = -5 (x + 2)^2 - 1$

Explanation:

Step1: Recall Quadratic Forms

• Intercept (Factored) Form: \( y = a(x - r_1)(x - r_2) \), where \( r_1, r_2 \) are roots.

\( y = -2(x + 4)(x - 7) \) matches this ( \( a=-2 \), roots at \( x=-4, x=7 \) ).

• Standard Form: \( y = ax^2 + bx + c \) ( \( a

eq0 \) ).
\( y = 2x^2 - 3x + 5 \) matches this ( \( a=2, b=-3, c=5 \) ).

• Vertex Form: \( y = a(x - h)^2 + k \), where \( (h,k) \) is the vertex.

\( y = -5(x + 2)^2 - 1 \) can be rewritten as \( y = -5(x - (-2))^2 + (-1) \), matching vertex form ( \( a=-5, h=-2, k=-1 \) ).

Step2: Match Each Equation

• \( y = -2(x + 4)(x - 7) \) → Intercept (Factored) Form
• \( y = 2x^2 - 3x + 5 \) → Standard Form
• \( y = -5(x + 2)^2 - 1 \) → Vertex Form

Answer:

• \( y = -2(x + 4)(x - 7) \) ↔ Intercept (factored) Form
• \( y = 2x^2 - 3x + 5 \) ↔ Standard Form
• \( y = -5(x + 2)^2 - 1 \) ↔ Vertex Form