Vertex Calculator

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**Step 1 :**

**Step 2 :**

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

Here the point (h, k) is called as vertex .

The general form of the quadratic function is f(x) =ax^{2} + bx + c.

To convert the standard form(y = ax^{2} + 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 - $\frac{b^{2}}{4a}$

To convert the standard form(y = ax

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.

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

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

h(x-coordinate) = $\frac{-b}{2a}$

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

Find the vertex of the parabola: y = 2x

^{2}+ 3x + 4?**Step 1 :**Given equation: y = 2x

^{2}+ 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)

Find the vertex of the parabola: y = x

^{2}+ 4x + 5?**Step 1 :**Given equation: y = x

^{2}+ 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

**Answer :**(h, k) = (-2, 1)

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).

**Answer :**Vertex is (0, 30).

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).

**Answer :**10.20 m.