Which of the following is a quadratic equation written in standard form?
A. - z² = 6z + 2
B. y² - 3y + 4 = 0
C. x - 3x² + 5 = 0
D. 2x² + 4x = 5
Answer (2)
The quadratic equation in standard form is option B, y 2 − 3 y + 4 = 0 . Options A, C, and D can be rearranged to demonstrate they are also quadratic equations, but B is already in the correct standard format. Therefore, B is the best answer.
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In this math problem, we are asked to identify which of the given equations is a quadratic equation in standard form.
A quadratic equation in standard form is written as:
a x 2 + b x + c = 0
Here, a , b , and c are constants, and x is the variable. The highest degree of the variable should be 2.
Let's examine the options given:
− z 2 = 6 z + 2 y 2 − 3 y + 4 = 0
This equation has two variables, z and y , and includes a term 2 y 2 . It is not a quadratic equation in standard form because it involves more than one variable and isn't arranged correctly.
0 x − 3 x 2 + 5 = 0
Rearranged, this becomes − 3 x 2 + 0 x + 5 = 0 , which is in standard quadratic form with a = − 3 , b = 0 , and c = 5 . However, 0 x can be omitted, simplifying the equation to − 3 x 2 + 5 = 0 . Since it follows the quadratic format a x 2 + b x + c = 0 , this is a quadratic equation in standard form.
2 x 2 + 4 x = 5
By rearranging to make one side zero, we have: 2 x 2 + 4 x − 5 = 0 . This is a quadratic equation in standard form with a = 2 , b = 4 , and c = − 5 , following the format a x 2 + b x + c = 0 .
Both options 2 and 3 are valid quadratic equations written in standard form, but if we choose only one, option 3 2 x 2 + 4 x − 5 = 0 is a clear quadratic equation in standard form.
