Question

1. the standard form of a quadratic function is

a) $a(x - h)^2 + k$ b) $ax + by = c$
c) $y - y_1 = m(x - x_1)$ d) $ax^2 + bx + c$

1. if a is negative in the function, which way does the parabola

a) up b) left
c) right d) down
35.
graph of a parabola on a coordinate grid
does this parabola have a maximum or minimum?
a) minimum b) maximum

Explanation:

Question 33

Step1: Recall quadratic function forms

The standard form of a quadratic function (vertex form) is \( a(x - h)^2 + k \), where \((h,k)\) is the vertex. Let's analyze each option:

• Option a: \( a(x - h)^2 + k \) is vertex (standard) form of quadratic.
• Option b: \( Ax + By = C \) is linear equation (standard form of line).
• Option c: \( y - y_1 = m(x - x_1) \) is point - slope form of line.
• Option d: \( ax^2+bx + c \) is the general (or standard in some contexts, but vertex form is more commonly referred to as standard for vertex - related properties) form, but the vertex - based standard form is \( a(x - h)^2 + k \).

Step1: Recall parabola direction rule

For a quadratic function in the form \( y=a(x - h)^2 + k \) (or \( y = ax^2+bx + c \)), the coefficient \( a \) determines the direction the parabola opens. If \( a>0 \), the parabola opens upward, and if \( a < 0 \), the parabola opens downward. When the parabola opens downward ( \( a<0 \) ), it has a maximum point at the vertex, and when it opens upward ( \( a > 0 \) ), it has a minimum point at the vertex. The question is about the direction when \( a \) is negative. Since \( a<0 \), the parabola opens down.

Step1: Analyze parabola opening direction

To determine if a parabola has a maximum or minimum, we look at the direction it opens. If the parabola opens upward (the "U" shape), it has a minimum value at the vertex. If it opens downward (the "n" shape), it has a maximum value at the vertex. Looking at the given graph, the parabola opens upward (it is a "U" - shaped curve). So, it has a minimum.

Answer:

a) \( a(x - h)^2 + k \)

Question 34