Question

Find the maximum or minimum value of$y=x^2-49$

Short answer

The minimum value of the quadratic is −49 and it occurs when x = 0 .

Step-by-step solution

Step 1. Given Information 

$y=x^2-49$

Step 2. Determining the type of parabola 

As value of a is positive, therefore it is a upward parabola.

Hence, it has a minimum value.

Step 3. Finding axis of symmetry.

$$\begin{gathered} x=-\frac{b}{2a} \\ \mathrm{as}b=0,x=0 \end{gathered}$$

Therefore, axis of symmetry : x = 0.

Step 4. Vertex of parabola

$$\begin{gathered} y\mathrm{when}x=0 \\ y=x^2-49 \\ ={\left(0\right)}^2-49 \\ =-49 \end{gathered}$$

Therefore vertex : (0,-49)

Step 5. Minimum value

Since the parabola has a minimum, the y-coordinate of the vertex is the

minimum y-value of the quadratic equation.

The minimum value of the quadratic is −49 and it occurs when x = 0 .

Step 6. Graph