Name: How to Draw the Graphs of Quadratic Equations
Uploaded: 2019-07-19
Duration: 5 min 10 s
Description: In this video, we will learn how to draw the graphs of quadratic equations with real coefficients using some examples. Let's understand the graph.

Question

A ball is thrown up into the air, from $5$ m above the ground. After $2$ seconds, the ball reaches a maximum height of $9$ m. It lands on the ground $5$ seconds after it was thrown. Find a quadratic function that models this situation. Write it in standard and vertex form.

Accepted Answer

A ball is thrown up into the air, from $5$ m above the ground. After $2$ seconds, the ball reaches a maximum height of $9$ m. It lands on the ground $5$ seconds after it was thrown.

Let $t$ and $h$ be the time and height respectively.

We know that, the vertex form of a Quadratic function is $y = a (x - t)^{2} + h, a \neq 0$ , where $(t, h) =$ Vertex.

Clearly, the maximum value occurs at $x = t$ and its value is given by $h$ .

So, according to the question, a ball is thrown up into the air from $5$ m above ground. After $2$ seconds i.e. $t = 2$ , ball reaches the maximum height of $9$ m i.e., $h = 9$

Since, the shape of graph is parabolic and it is opening downwards.

Therefore, the required quadratic function is $y = - (x - 2)^{2} + 9$

$\Rightarrow y = - (x^{2} - 4 x + 4) + 9$

$\Rightarrow y = 5 + 4 x - x^{2}$

Hence, the standard and vertex forms are: $y = 5 + 4 x - x^{2}; y = - (x - 2)^{2} + 9$ .

A ball is thrown up into the air, from $5$ m above the ground. After $2$ seconds, the ball reaches a maximum height of $9$ m. It lands on the ground $5$ seconds after it was thrown. Find a quadratic function that models this situation. Write it in standard and vertex form.

Important Questions on A Parable About Parabolas (Quadratic Functions in 2D Space)

Learn and Prepare for any exam you want !

A ball is thrown up into the air, from 5 m above the ground. After 2 seconds, the ball reaches a maximum height of 9 m. It lands on the ground 5 seconds after it was thrown. Find a quadratic function that models this situation. Write it in standard and vertex form.

Important Questions on A Parable About Parabolas (Quadratic Functions in 2D Space)

Learn and Prepare for any exam you want !

A ball is thrown up into the air, from $5$ m above the ground. After $2$ seconds, the ball reaches a maximum height of $9$ m. It lands on the ground $5$ seconds after it was thrown. Find a quadratic function that models this situation. Write it in standard and vertex form.