Answer:
Step-by-step explanation:
To describe the graph of the function y=[tex]2x^2 + 12x - 15[/tex].
The function y=[tex]2x^2 + 12x - 15[/tex] is a quadratic function. All quadratic function have a parabolic curve. The direction to which the parabola opens is determined by the coefficient of [tex]x^2[/tex], If the coefficient of [tex]x^2[/tex], is positive as in the case above, the graph forms a downward "U" shape.
The solutions of the function y=[tex]2x^2 + 12x - 15[/tex] are 1.06 and -7,06, This means the graph intersects the x-axis at points 1.06 and -7.06.
To determine the axis of symmetry of a downward facing parabola,
We use the equation: [tex]x=-\frac{b}{2a}[/tex]
a=2, b=12.
Axis of Symmetry=[tex]-\frac{12}{2X2}=-3[/tex]
The minimum point is the value of y at the axis of symmetry.
[tex]f(-3)=2(-3)^2 + 12(-3) - 15=-33[/tex]
