2-1 through 2-3

What is the vertex of the graph of the function 𝘧(𝘹)=𝘹²−𝟪𝘹+𝟧?

(4, 11)

Vertex: (−𝟦,−𝟧) Axis of Symmetry: 𝘹=−𝟦 Maximum: 𝘺=−𝟧 Domain: (−∞,∞) Range: (−∞,−𝟧)

Identify the vertex, axis of symmetry, minimum or maximum, domain, and range of the function 𝘧(𝘹)=−(𝘹+𝟦)²−𝟧

What is the equation of a parabola that passes through the points (−𝟮,𝟯𝟮) , (𝟭,𝟱) , and (𝟯,𝟭𝟳) ? (1/2)

Steps 3 and 4 on next slide

The value of h determines the horizontal translation.

What does the value of h represent in f(x) = a(x-h)² + k?

The value of k determines the vertical translation.

What does the value of k represent in f(x) = a(x-h)² + k?

(h,k) h is x, k is y

in the vertex form (f(x) = a(x-h)² + k) what represents the vertex of the parabola?

f(x) = ax² + bx + c

standard form of quadratic eq.

A baseball is thrown from the upper deck of a stadium, 128 ft above the ground. The function 𝘩(𝘵)=−𝟣𝟨𝘵²+𝟥𝟤𝘵+𝟣𝟤𝟪 gives the height of the ball t seconds after it is thrown. How long will it take the ball to reach the ground?

the ball will hit the ground in 4 seconds

f(x) = a(x-h)² + k

vertex form of a quadratic eq.

What is the equation of j? Write the equation in vertex form and in the form 𝘺=𝘢𝘹²+𝘣𝘹+𝘤. Let j be a quadratic function whose graph is a reflection of the graph of f in the x-axis followed by a translation 1 unit down.

The equation is 𝘫(𝘹)=−𝘹²−1

What is the equation of a parabola that passes through the points (𝟤,−𝟣𝟤), (−𝟣,−𝟣𝟧) (−𝟦,−𝟫𝟢)?

The equation that goes through the three points is 𝘺=−𝟦𝘹²+𝟧𝘹−𝟨

The equation representing the height of the flying disk is 𝘺=−𝟥/𝟤(𝘹−𝟤)²+𝟣𝟢, or 𝘺=−𝟥/𝟤𝘹²+𝟨𝘹+𝟦

The graph shows the height of the flying disk with respect to time. What is the equation of the function? Write the equation in vertex form. Then write the equation in the form 𝘺=𝘢𝘹²+𝘣𝘹+𝘤

all real numbers

What is the domain of 𝘧(𝘹) = 𝟤(𝘹 − 𝟥)² + 𝟦?

Step 1 Substitute the coordinates of the vertex for h and k in the vertex form of a quadratic function. (𝘩,𝘬) = (−𝟤,𝟥), so 𝘺 = 𝘢(𝘹−(−𝟤))² + 𝟥 Step 2 Substitute the values of x and y from the y-intercept, and then solve for a. (𝘹,𝘺) = (𝟢,−𝟣), 𝗌𝗈 = 𝘢(𝟢+𝟤)²+𝟥 a = -1 Substitute the value of a into the vertex form of a quadratic function. 𝘢 = −1, so 𝘺=−(𝘹+𝟤)²+𝟥 The equation of the parabola is 𝘺 = −(𝘹+𝟤)²+ 𝟥

What is the equation of a quadratic function with vertex (-2, 3) and y-intercept -1?

The equation is 𝘫(𝘹)=(𝘹−𝟤)²−𝟧 or 𝘫(𝘹)=𝘹²−𝟦𝘹−𝟣

What is the equation of j? Write the equation in vertex form and in the form 𝘺=𝘢𝘹²+𝘣𝘹+𝘤. Let j be a quadratic function whose graph is a translation 2 units right and 5 units down of the graph of f.

The range is 𝘺≥𝟦

What is the range of 𝘧(𝘹) = 𝟤(𝘹 − 𝟥)² + 𝟦?