Q11. - Algebra 1

Question

Which is an equation for the function shown in the graph?

A $y=-3x^2$

B $y=3x^2+1$

C $y=x^2+2$

D $y=-3x^2+2$

Step-by-Step Solution

Answer

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

Step 1. Define the concept.

In a quadratic equation $y=a{x}^2+bx+c$, 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 $\left(0,2\right)$.

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

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