Chapter 9: Q18. (page 566)

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

Short Answer

Expert verified

Option D is the correct choice.

Step by step solution

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

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

Step 2. Define the graph of a function.

The graph of a function is the set of all points whose coordinates $(x, y)$ satisfy the function $y = f (x)$ .

Step 3. Write an equation for the function shown in the graph.

Observe the graph shown in the figure.

The graph of the parabola opens downward, so the coefficient of $x^{2}$ must be negative.

We can ignore the options B and C, where the coefficient of $x^{2}$ is positive.

The vertex of the parabola is $(0, 1)$ , in the option A: $y = - 2 x^{2}$ , the vertex is $(0, 0)$ . So, option A is not the correct choice.

Option D: $y = - 2 x^{2} + 1$ has the vertex at $(0, 1)$ and it opens downward.

Therefore, option D is the correct choice.

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

Short Answer

Step by step solution

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

Step 2. Define the graph of a function.

Step 3. Write an equation for the function shown in the graph.

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

Short Answer

Step by step solution

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

Step 2. Define the graph of a function.

Step 3. Write an equation for the function shown in the graph.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Mechanics Maths

Theoretical and Mathematical Physics

Applied Mathematics

Calculus

Logic and Functions

Study anywhere. Anytime. Across all devices.

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