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Vertex Calculator
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The curve parabolas always have the lowest point if the parabola is downside-up or the highest point if the parabola is upside-down. The point where the curve transforms its path is called as "vertex".
The vertex form of the function is:
y = a(x - h)2 + k
Here the  point (h, k) is called as vertex .
The general form of the quadratic function is f(x) =ax2 + bx + c.
To convert the standard form(y = ax2 + bx + c) of a  function into vertex form(y = a(x - h)2 + k), we have to write the equation in the complete square form and vertex(h, k) is given by:
h = $\frac{-b}{2a}$
k = c - $\frac{b^{2}}{4a}$

Vertex form Calculator (vertex calculator) is a online tool to calculate the value of coordinates of the vertex (h,k). You just have to enter the value of a, b and c and use the vertex form converter to get the vertex instantly. It is a online calculator that known as standard form to vertex form calculator which acts as a vertex finder or a tool to find the vertex calculator.

## Steps for Vertex Calculator

Step 1 :

Observe the standard equation and note down the value of a, b and c.

Step 2 :

To find vertex(h, k), use the formula:

h(x-coordinate) = $\frac{-b}{2a}$
k(y - coordinate) = c - $\frac{b^{2}}{4a}$

## Problems on Vertex Calculator

1. ### Find the vertex of the parabola: y = 2x2 + 3x + 4?

Step 1 :

Given equation: y = 2x2 + 3x + 4

a = 2, b = 3 and c = 4

Step 2 :

Vertex(h, k) is given by

h = $\frac{-b}{2a}$$\frac{-(3)}{2(2)} = \frac{-3}{4} = -0.75 k = c - \frac{b^{2}}{4a} = 4 - \frac{(3)^{2}}{4(2)} = 4 - \frac{9}{8} = 4 - 1.12500 = 2.87500 Answer : (h, k) = (-0.75, 2.87500) 2. ### Find the vertex of the parabola: y = x2 + 4x + 5? Step 1 : Given equation: y = x2 + 4x + 5 a = 1, b = 4 and c = 5 Step 2 : Vertex(h, k) is given by h = \frac{-b}{2a}$$\frac{-(4)}{2(1)}$ = $\frac{-4}{2}$  = -2

k = c - $\frac{b^{2}}{4a}$ = 5 - $\frac{(4)^{2}}{4(1)}$ = 5 - $\frac{16}{4}$ = 5 - 4 = 1

(h, k) = (-2, 1)

3. ### A manufacturing company designed a parabolic arch in a memorial park. The center of the curve is located on the y-axis. The height of the arch is 30 feet. What will be the vertex of the arch.

Step 1 :

Let vertex is represented as (h, k).

Since center of arch is located on y-axis. It means h-coordinate is zero, i.e. h = 0

Height of the arch = 30 feet

Step 2 :

So k = 30

$\therefore$  The vertex will be at, (h, k) = (0, 30).

Vertex is (0, 30).

4. ### During a JEE admission test, a student asked to find the maximum height of an object, which is thrown vertically upward with velocity of 20 m/sec. The displacement after some seconds is given by: S = -gt$^2$ + 20t. Find the maximum distance covered by the object.

Step 1 :

We are given with the displacement equation, S = -gt$^2$ + 20t.

Compare with standard form of the quadratic equation, ax$^2$ + bx + c, we get

a = -9.8, b = 20 and c = 0  (because g = 9.8 m/sec$^2$ )

=> t = $\frac{-b}{2b}$ = 1.020

Step 2 :

Maximum height is reached after 1.020 sec. The maximum height is

S = -9.8 * (1.020)$^2$ + 20 * 1.020

S = 10.20 (Solve it).