Question: In a quadratic equation, if the coefficient of x^2 is negative, what can be inferred about the graph?
Options:
It opens upwards.
It opens downwards.
It has no real roots.
It is a straight line.
Correct Answer: It opens downwards.
Solution:
A negative coefficient for x^2 indicates that the parabola opens downwards.
In a quadratic equation, if the coefficient of x^2 is negative, what can be infe
Practice Questions
Q1
In a quadratic equation, if the coefficient of x^2 is negative, what can be inferred about the graph?
It opens upwards.
It opens downwards.
It has no real roots.
It is a straight line.
Questions & Step-by-Step Solutions
In a quadratic equation, if the coefficient of x^2 is negative, what can be inferred about the graph?
Step 1: Understand what a quadratic equation is. It is usually in the form of ax^2 + bx + c, where a, b, and c are numbers.
Step 2: Identify the coefficient of x^2, which is 'a'.
Step 3: Check if 'a' is negative. A negative number is less than zero.
Step 4: Know that if 'a' is negative, the shape of the graph is a parabola.
Step 5: Learn that a parabola with a negative 'a' opens downwards, like an upside-down U.
Parabola Orientation – In a quadratic equation of the form ax^2 + bx + c, the sign of the coefficient 'a' determines the direction in which the parabola opens. A negative 'a' means the parabola opens downwards.
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