Writing quadratic equations in vertex form worksheet

Q: How do you write a vertex equation?

We can use the vertex form to find a parabolas equation. The idea is to use the coordinates of its vertex (maximum point, or minimum point) to write its equation in the form y=a(x−h)2+k (assuming we can read the coordinates (h,k) from the graph) and then to find the value of the coefficient a.

Problem 1 :

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Detailed Answer Key
How do you write a quadratic equation in vertex form?
How do you do vertex form step by step?
How do you write a vertex equation?
How do you write a quadratic equation?

Write the following quadratic function in vertex form and sketch the parabola.

y = x2 - 4x + 3

Problem 2 :

Write the following quadratic function in vertex form and sketch the parabola.

y = 2x2 - 8x + 9

Detailed Answer Key

Problem 1 :

Write the following quadratic function in vertex form and sketch the parabola.

y = x2 - 4x + 3

Solution :

Step 1 :

In the quadratic function given, the coefficient of x2 is 1. So, we can skip step 1.

Step 2 :

In the quadratic function y = x2 - 4x + 3, write the "x" term as a multiple of 2.

Then,

y = x2 - 2(x)(2) + 3

Step 3 :

Now add and subtract 22 on the right side to complete the square.

Then,

y = x2 - 2(x)(2) + 22 - 22 + 3

y = x2 - 2(x)(2) + 22 - 4 + 3

y = x2 - 2(x)(2) + 22 - 1

Step 4 :

In the result of step 3, if we use the algebraic identity

(a - b)2 = a2 - 2ab + b2

on the right side, we get

y = (x - 2)2 - 1

The quadratic function above is in vertex form.

Comparing

y = (x - 2)2 - 1

and

y = a(x - h)2 + k,

the vertex is

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

and

a = 1

Graph of the Parabola :

The vertex of the parabola is (2, -1). Because the sign of "a" is positive the parabola opens upward.

Problem 2 :

Write the following quadratic function in vertex form and sketch the parabola.

y = 2x2 - 8x + 9

Solution :

Step 1 :

In the quadratic function given, the coefficient of x2 is 2. So, factor "2" from the first two terms of the quadratic expression on the right side.

y = 2(x2 - 4x) + 9

Step 2 :

In the quadratic function y = 2(x2 - 4x) + 9, write the "x" term as a multiple of 2.

Then,

y = 2[x2 - 2(x)(2)] + 9

Step 3 :

Now add and subtract 22 inside the parentheses to complete the square.

Then,

y = 2[x2 - 2(x)(2)+ 22 - 22] + 9

y = 2[x2 - 2(x)(2)+ 22 - 4] + 9

Step 4 :

In the result of step 3, if we use the algebraic identity

(a - b)2 = a2 - 2ab + b2

inside the parentheses, we get

y = 2[(x - 2)2 - 4] + 9

y = 2(x - 2)2 - 8 + 9

y = 2(x - 2)2 + 1

The quadratic function above is in vertex form.

Comparing

y = 2(x - 2)2 + 1

and

y = a(x - h)2 + k,

the vertex is

(h, k) = (2, 1)

and

a = 2

Graph of the Parabola :

The vertex of the parabola is (2, 1). Because the sign of "a" is positive the parabola opens upward.

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How do you write a quadratic equation in vertex form?

The vertex form of a quadratic function is f(x) = a(x – h)2 + k, where a, h, and k are constants. of the parabola is at (h, k).

How do you do vertex form step by step?

The standard form of a parabola is y = ax2 + bx + c and the vertex form of a parabola is y = a (x - h)2 + k. Here, the vertex form has a square in it. ... Standard Form to Vertex Form..

How do you write a vertex equation?

We can use the vertex form to find a parabola's equation. The idea is to use the coordinates of its vertex (maximum point, or minimum point) to write its equation in the form y=a(x−h)2+k (assuming we can read the coordinates (h,k) from the graph) and then to find the value of the coefficient a.