Chapter 9: Q11. (page 597)

Which is an equation for the function shown in the graph?
A $y = - 3 x^{2}$
B $y = 3 x^{2} + 1$
C $y = x^{2} + 2$
D $y = - 3 x^{2} + 2$

Short Answer

Expert verified

Option $D : y = - 3 x^{2} + 2$ is the correct choice.

Step by step solution

Step 1. Define the concept.

In a quadratic equation $y = a x^{2} + b x + c$ , if the coefficient of $x^{2}$ is positive, then the graph of the parabola is upward open and vertex is at minimum and if the coefficient of $x^{2}$ is negative, then the graph of the parabola is downward open and vertex is at maximum.

Step 2. Graphical representation of the quadratic functions.

The graph of any quadratic function is a parabola.

Step 3. State interpretation of the given graph.

Downward open parabola means the coefficient of $x^{2}$ is negative. So, we can ignore the options B and C.

Now the vertex of the parabola is $(0, 2)$ .

Since in Option $A : y = - 3 x^{2}$ the equationhas the vertex at origin or $(0, 0)$ , therefore, this option is not valid.

In option $D : y = - 3 x^{2} + 2$ , the coefficient is negative and it also satisfies the coordinates $(0, 2)$ , therefore, option $D : y = - 3 x^{2} + 2$ is the correct choice.

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Which is an equation for the function shown in the graph?
A $y = - 3 x^{2}$
B $y = 3 x^{2} + 1$
C $y = x^{2} + 2$
D $y = - 3 x^{2} + 2$

Short Answer

Step by step solution

Step 1. Define the concept.

Step 2. Graphical representation of the quadratic functions.

Step 3. State interpretation of the given graph.

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Which is an equation for the function shown in the graph?Ay=−3x2By=3x2+1Cy=x2+2Dy=−3x2+2

Short Answer

Step by step solution

Step 1. Define the concept.

Step 2. Graphical representation of the quadratic functions.

Step 3. State interpretation of the given graph.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Calculus

Statistics

Logic and Functions

Mechanics Maths

Probability and Statistics

Study anywhere. Anytime. Across all devices.

Which is an equation for the function shown in the graph?
A $y = - 3 x^{2}$
B $y = 3 x^{2} + 1$
C $y = x^{2} + 2$
D $y = - 3 x^{2} + 2$