Quadratic from a Point and X Intercepts

The solutions of a quadratic equation are known as the _____.

• Vertices

• Roots

• Squares

• Formulas

Does this graph in the back have maximum or minimum value?

• maximum

• minimum

• neither

• both

Tags

CCSS.HSF-IF.C.7A

What is the shape of the quadratic called?

• That "U" shape

• There's a name for it?

• Parabola

• No hablo Ingles

Tags

CCSS.HSF-IF.C.7A

Which equation could possibly represent this parabola?

Tags

CCSS.HSF-IF.C.7A

Which is these equations is a quadratic function?

• f(x)=2x+5

• f(x)=2^x

• f(x)=(x+1)³

• f(x)=(x-5)²

The domain for every parabola

• All real numbers

• Positive integers

• Negative integers

• Depends on the parabola

Write a quadratic equation given the x intercepts and one other point.

Step 1: Write the factors.

The intercepts of this function are (6, 0) and (8, 0). Write the factors.

• (x-6) and (x-8)

• (x+6) and (x+8)

• (x-6) and (x+8)

• (x+6) and (x-8)

Tags

CCSS.HSA-SSE.B.3B

CCSS.HSF-IF.C.8A

Write a quadratic equation given the x intercepts and one other point.

Step 2: Find a.

Now that you know that the factors are (x-6) and (x-8), you must find a. Plug the coordinates of the vertex (7, 1) in for x and y and solve for a.

y = a(x-6)(x-8)

What is the value of a?

• a = 1

• a = -1

• a = 7

• a = -7

Write a quadratic equation given the x intercepts and one other point.

Step 3: Write the equation in factored form.

Now, you know that the factors are (x-6) and (x-8) and a = -1. Write the equation of the graph in factored form.

• -(x-6)(x-8)

• -(x+6)(x+8)

• (x-6)(x+8)

• (x+6)(x-8)

Write a quadratic equation given the x intercepts and one other point.

Put the steps together.

1. Find the factors.
2. Solve for a by substituting in the extra point.
3. Write the equation in factored form.

The roots of the function are (-3, 0) and (5, 0).

The point (4, -3) is also on the graph.

• y=4(x+3)(x-5)

• y=3/7(x-3)(x+5)

• y=-3(x-3)(x+5)

• y=3/7(x+3)(x-5)