In a function f(x) = ax^2 + bx + c, if a > 0, what can be said about the grap

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Question: In a function f(x) = ax^2 + bx + c, if a > 0, what can be said about the graph of the function?

Options:

Correct Answer: It opens upwards.

Solution:

If a > 0 in a quadratic function, the graph opens upwards, indicating that it has a minimum point.

In a function f(x) = ax^2 + bx + c, if a > 0, what can be said about the graph of the function?

In a function f(x) = ax^2 + bx + c, if a > 0, what can be said about the graph of the function?

Step 1: Identify the function type. The function f(x) = ax^2 + bx + c is a quadratic function because it has x squared (x^2).
Step 2: Look at the coefficient 'a'. In the function, 'a' is the number in front of x^2.
Step 3: Check the value of 'a'. If 'a' is greater than 0 (a > 0), it means 'a' is a positive number.
Step 4: Understand what a positive 'a' means for the graph. A positive 'a' means the graph of the function will open upwards, like a U shape.
Step 5: Identify the minimum point. Since the graph opens upwards, it will have a lowest point, called the minimum point.

Quadratic Functions – Understanding the shape and properties of the graph of a quadratic function based on the coefficient of the x^2 term.
Graph Behavior – Recognizing how the sign of the leading coefficient (a) affects the direction in which the parabola opens.
Minimum and Maximum Points – Identifying the nature of the vertex of the parabola based on the leading coefficient.