Question

a coordinate grid is mapped onto a video game screen, with the origin at the lower left corner. the game designer programs a turtle to move along a linear path that passes through the points (0, 0) and (10, 8). the designer also programs a bird with a path that can be modeled by a quadratic function. the bird starts at the vertex of the path at (0, 20) and passes through the point (10, 8). what is the slope of the line that represents the turtles path? 0.8 complete what are the values of the constants in the vertex form of the quadratic equation that models the birds path? h = 1 k = a = done

Explanation:

Step1: Recall vertex form of quadratic

The vertex form of a quadratic function is \( y = a(x - h)^2 + k \), where \((h, k)\) is the vertex. The bird's path starts at vertex \((0, 20)\), so \( h = 0 \), \( k = 20 \).

Step2: Substitute vertex and point

Substitute \( h = 0 \), \( k = 20 \), and the point \((10, 8)\) into \( y = a(x - h)^2 + k \). We get \( 8 = a(10 - 0)^2 + 20 \).

Step3: Solve for \( a \)

Simplify the equation: \( 8 = 100a + 20 \). Subtract 20 from both sides: \( 8 - 20 = 100a \), so \( -12 = 100a \). Divide by 100: \( a = \frac{-12}{100} = -0.12 \).

Answer:

\( h = 0 \), \( k = 20 \), \( a = -0.12 \)