# How do you write a quadratic function in standard form whose graph passes through points (1/2, -3/10), (1, 6/5), (1/4, -3/10)?

##### 1 Answer

Start with the vertex form and use symmetry to find the x coordinate.

Use the points to find the other 2 two values of the vertex form.

Expand the vertex form into the standard form.

#### Explanation:

Because you specified a function we discard the vertex form

Because the we know the 2 x values corresponding to y value,

Substitute

Substitute the point

Substitute the point

Subtract equation [3] from equation [4]:

Use equation [3] to find the value of k:

Substitute the value of "a" and "k" into equation [2]:

Expand the square:

Distribute the 4:

This is the standard form:

The following is a graph of the equation and the 3 points: