Q3. - Algebra 1

Question

State whether the given sentence is true or false. If false, replace the underlined term to make a true sentence.

The graph of a quadratic function is a straight line.

Step-by-Step Solution

Answer

The sentence, “The graph of a quadratic function is a straight line” is false.

The correct replacement for the underlined term to make a true sentence is the parabola.

Step 1. Define the standard form of the quadratic function.

A quadratic function, which is written in the form, $y=a{x}^2+bx+c$, where, $a\ne 0$ is called the standard form of the quadratic function.

Step 2. Define a straight-line function.

The function having a degree of 1 is called a straight line function.

Step 3. Check whether the given sentence is true or false.

The quadratic function $y=a{x}^2+bx+c$ has a degree of 2 and is called a parabola.

The graph of a parabola has a curved shape.

So, the graph of a quadratic function is a parabola.

Therefore, the sentence, “The graph of a quadratic function is a straight line” is false.

The correct replacement for the underlined term to make a true sentence is the parabola.